gene clustering

7182019 Gene Clustering

httpslidepdfcomreaderfullgene-clustering 176

Gene clustering

Gene sorting



Outline

Clustering

K-means

Annealed K-means

Kohonenrsquos Self -organizing algorithm

Yeast gene analysis

Cancer gene analysis



High dimensional data clustering

K-means

Annealed K-Means

Euclidean distance measure

Mahalanobis distance measure



Data clustering

Find cluster centers



Matlab stats toolbox

Add directory toolboxstats to matlab path

Load data_9mat

Kmeans clustering

[cidx ctrs] = kmeans(XX10)

plot(XX(1)XX(2))

hold onplot(ctrs(1)ctrs(2)ro)





Ten clusters

Data matrix Nxd

Center locations Kxd

Membership Nx1



Download

Internet

Example Add directory cluster to matlab path

Load data_9mat

Kmeans clustering [cidx ctrs] = kmeans(XX10)

plot(XX(1)XX(2))hold onplot(ctrs(1)ctrs(2)ro)

My_Kmeans Parallel codes




Ten clusters

Data matrix dxN

Center locations dxK

Membership 1xN



K-means

An iterative approach

Non-overlapping partition

Means of partitioned groups

Non-overlapping partition Each data x

is partitioned to its nearest center



Stepwise procedure

1 Input unsupervised high dimensional data

and the number K of clusters

2 Randomly initialize K centers near the center

of given data3 Partition all data to K clusters using current

means

4 Update the center position of each group5 If halting condition holds exit

6 Go to step 3



Exercise

Draw a while-loop flow chart to illustrate

how the K-means algorithm partitions

high-dimensional data to K clusters



Exercise

Apply the K-means method to clustering

analysis of data in data_25mat

Calculate the mean distance between

each data point and its correspondent

center



Annealed K-means

Use overlapping memberships

Overcome the local minimum problem

Relaxation under an annealing process



Overlapping memberships

Each x has an overlapping membership

to each cluster

The membership to the ith cluster is

proportional to exp(-βdi) where di denote

the distance between x and the ith center



Annealed K-means

1 Input unsupervised high dimensional dataand the number K of clusters

2 Set β to sufficiently small positive numberrandomly initialize K centers near the center

of given data3 Determine overlapping memberships of all

data to K clusters

4 Update the center position of each group

5 Increase β carefully 6 If halting condition holds exit

7 Go to step 3



Exercise


how the annealed K-means algorithm

partition high-dimensional data to K

clusters

Implement the flow chart using Matlab

codes



Set β sufficiently small

Input all xt Set K

Halting

condition

Determine overlapping membership

of each xt

Update each yk

Increase β carefully

exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d



Overlapping membership

Sufficiently small β

vk equals 1K

Sufficiently large β

vk = 1 if dk = mini di

= 0 otherwise

All vk are determined by the winner-take-all

principle



Why annealing

Sufficiently large β leads to the K-means

algorithm

Can annealing improve the performance

How to measure the performance for

clustering



center nearestthe][eachof distancetheupsums

10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx



Criterion of K-means

Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance

Refer to Math Programming



Self-organization

Clustering

Define neighboring relations of clusters

on a 2D lattice

Sorting high-dimensional data on a

lattice



Clustering by SOM



SOM

Download Matlab Neural Networks

toolbox

Add directory nnet with sub-directories

to matlab path

Apply the SOM method to clustering




Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM

net = newsom([0 02 0 01][5 5]gridtop)nettrainParamepochs=100

Initialization

net = train(netXX)

plotsom(netiw11netlayers1distances)

Training

Display



net = newsom([0 02 0 01][5 5]gridtop)

5x5 lattice

2x2 matrix for two-dimensional inputs

dx2 matrix for d-dimensional inputs



net = train(netXX)

dxN data matrix



Surface construction

demo_fr2_somm



Surface reconstruction

P = rand(22000)4-2f = exp(-sum(P^2))P =[Pf]

net = newsom([0 02 0 01 0 01][10 10]gridtop)plotsom(netlayers1positions)nettrainParamepochs=100net = train(netP)plot3(P(1)P(2)P(3)g)

hold onplotsom(netiw11netlayers1distances)



Self-organization

Maximal fitting and minimal wiring

principle

Sort high dimensional data on a 2D

lattice



Neural optimization

K-means

Minimal distance to the nearest center

Kohonenrsquos self -organizing

Minimal wiring distance between

neighboring centers



Neighboring relations on a lattice

An M-by-M lattice

A node is indexed by (ij) ij=1hellipM

C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4



If (ij) not within S1-S4 and C1-C4

NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)

NB(ij) can be separately defined if (ij)belongs S1- S4 and C1-C4



Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(



Kohonenrsquos self -organizing algorithm

Self-organizing map - Wikipedia the free

encyclopedia

Neural networks (1996)


Neurocomputing (2011)



SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)



Neurocomputing 74(12-13) 2228-2240

(2011)

Minimal wiring and maximal fitting




criteria

Maximal fitting to a center Minimal distance to the nearest center

Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)



Set β sufficiently small Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight distance

k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx

















Microarray expressions of yeast genes

Pat_Brown_Lab_Home_Page

Exploring the Metabolic and Genetic Control of Gene




Expression on a Genomic Scale



Load gene matrix

Load yeastdata822

Genes(1020)Display names of genesnumbered between 10 and 20

Gene matri 822 7



Gene matrix 822x7

Gene id



Problem

Apply the k-means algorithm to processdata_25

Apply the annealed k-means algorithm to

process data_25 Numerical simulations for comparisons

of the two algorithms

Quantitative evaluations Statistics of mean and variance summarized

over 10 executions



Problem

Apply the k-means algorithm to processyeast_822


process yeast_822 Numerical simulations for comparisons



over 10 executions

G l t i b k



Gene clustering by kmeans

Load data

load yeastdata822mat

times=[0 95 115 135 155 175 195]

plot(timesyeastvalues)

G l t i b k




Kmeans analysis

for c = 116subplot(44c)plot(timesyeastvalues((cidx == c)))

end

Display

Genes belongingthe second cluster

[cidx ctrs] = kmeans(yeastvalues 16)

genes(cidx==2)

E i f 16 l t



Expressions of 16 gene clusters

St ti ti l D d



Statistical Dependency

load yeastdata822matX=yeastvalues

XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K



Problem Yeast_ICA_Kmean

Apply Jade_ICA to translate yeast data to

independent components

Is it reasonable to employ Euclidean distance

to measure similarity of genes What is the impact of ICA on gene clustering

Numerical simulations

ICA

Annealed k-means clustering

Describe clusters of genes

P bl



Problem

Apply the Kohonenrsquos self -organizing

algorithm to sort yeast_822 on a lattice

Refer to Neurocomputing 74(12-13)

2228-2240 (2011)

Visualize yeast gene expressions at

each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)

yeast822_som_20x20matdemo_gene_somm

C Di t



Centers=netiw11

Y=Centers

X=P

M=size(Y1)N=size(X1)

A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i



Cross_Distance Matrix

D 822x400

Cross distances between 822 genes and

400 gene centers

400 clusters

Q



Query

How many genes in each cluster

Which cluster a gene belongs

[xx ind]=min(D)

sum(ind==k) how many genes in the kth cluster

ind(i)

Vi li ti f d it



Visualization of gene density

[xx ind]=min(D) K=20 M=K^2

for k=1M

num(k)=sum(ind==k) how many genes in the kth cluster

end

a = linspace(-11K)

x = []for i=1K

xx = [ones(201)a(i) a]

x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)

Visualization of gene expressions




Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K

xx = [ones(201)a(i) a]x = [x xx]

end

time = 1

y = Y( time) x=x

Problem



Problem

Apply ICA to translate yeast_822 to


Apply SOM to process independent

components of yeast_822


each time course

Problem



Problem

Apply ICA to translate yeast_822 toindependent components

Apply annealed SOM to process

independent components of yeast_822


each time course



Outline

Clustering

K-means

Annealed K-means

Kohonenrsquos Self -organizing algorithm

Yeast gene analysis

Cancer gene analysis




K-means

Annealed K-Means





Data clustering






Load data_9mat

Kmeans clustering


plot(XX(1)XX(2))






Ten clusters

Data matrix Nxd


Membership Nx1



Download

Internet


Load data_9mat







Ten clusters

Data matrix dxN


Membership 1xN



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




K-means

Annealed K-Means





Data clustering






Load data_9mat

Kmeans clustering


plot(XX(1)XX(2))






Ten clusters

Data matrix Nxd


Membership Nx1



Download

Internet


Load data_9mat







Ten clusters

Data matrix dxN


Membership 1xN



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Data clustering






Load data_9mat

Kmeans clustering


plot(XX(1)XX(2))






Ten clusters

Data matrix Nxd


Membership Nx1



Download

Internet


Load data_9mat







Ten clusters

Data matrix dxN


Membership 1xN



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course





Load data_9mat

Kmeans clustering


plot(XX(1)XX(2))






Ten clusters

Data matrix Nxd


Membership Nx1



Download

Internet


Load data_9mat







Ten clusters

Data matrix dxN


Membership 1xN



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course





Ten clusters

Data matrix Nxd


Membership Nx1



Download

Internet


Load data_9mat







Ten clusters

Data matrix dxN


Membership 1xN



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Download

Internet


Load data_9mat







Ten clusters

Data matrix dxN


Membership 1xN



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




Ten clusters

Data matrix dxN


Membership 1xN



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



K-means








Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Stepwise procedure





means


6 Go to step 3



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Exercise






Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Exercise





center



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Annealed K-means








to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course





to each cluster






Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Annealed K-means




data to K clusters



7 Go to step 3



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Exercise




clusters


codes




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




Input all xt Set K

Halting

condition


of each xt

Update each yk


exit

Y



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Minimize the weight

distance

t

i

t

i

i

t

i

i

i

t

iii

t v

t t v

t t v

dy

dE

t t v

][

][][

0)][(][

0

][][E

i

2

x

y

yx

yx



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



k

k

k

k

k

k

k k

k k

d C

d C

v

d C vd v

)exp(1

1)exp(

1

)exp()exp(



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



j

j

k

k d

d v

)exp(

)exp()(

d





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course





vk equals 1K



= 0 otherwise


principle



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Why annealing


algorithm



clustering




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




10][][

][][

][][

EE

][][E

i

2

2

2

tot E

t vt if

t t v

t t v

t t v

i

t i

ii

i t

ii

i

i

t

iii

x

yx

yx

yx




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




Minimal distance to

the nearest center

t i

ii t t 2][][E(y) yx



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Cross distance




Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Self-organization

Clustering


on a 2D lattice


lattice



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Clustering by SOM



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



SOM


toolbox


to matlab path





Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Load data

load data_25

plot(XX(1)XX(2)g)

hold on



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



SOM


Initialization

net = train(netXX)


Training

Display




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




5x5 lattice





net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



net = train(netXX)

dxN data matrix




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




demo_fr2_somm









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course









Self-organization


principle


lattice



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Neural optimization

K-means




neighboring centers




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




An M-by-M lattice


C1 i=1j=1

C2 i=1j=M

C3 i=Mj=1

C4 i=Mj=M

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




An M-by-M lattice


S1 i=1j=2M-1

S2 i=2M-1j=M

S3 i=Mj=2M-1

S4 i=2M-1j=1

Corner 3

Corner 2

Corner 4

Corner 1 Side 1

Side 2

Side 3

Side 4




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




NB(ij)= (i-1j)(i+1j)(ij-1)(i j+1)




Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Wiring Criterion

j M i jih

y yk k NB ji k jih

)1()(

W2

)()( )(





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course





encyclopedia






SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



SOM matlab toolbox

SOM Toolbox



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Neural Networks 15(3) 337-347 (2002)




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




(2011)





criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




criteria


Wiring Criterion

t i

ii t t 2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W

2

)()(

)(





criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




criteria

t iii t t

2

][][E(y) yx

j M i jih

y yk k NB ji

k jih

)1()(

W2

)()(

)(

WEF(y)




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




Halting

condition


of each xt

Update each yk


exit

Y




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




k

k NBh

k hk

t

k

i

k k

k NBh

k h

t

ik k

ySolve

y yt t v

dy

W E d

y yt t v

0)()][(][

0)(

W][][E

)(

)(

2

k

2

yx

yx


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course


























Load gene matrix

Load yeastdata822


Gene matri 822 7



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Gene matrix 822x7

Gene id



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Problem






over 10 executions



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Problem






over 10 executions

G l t i b k




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




Load data


times=[0 95 115 135 155 175 195]


G l t i b k




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




Kmeans analysis


end

Display



genes(cidx==2)

E i f 16 l t




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




St ti ti l D d





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course





XX=X

W=jader(XX)

Y=WXX

X=Y

yeast_ICA_kmeansm

P bl Y t ICA K









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course









ICA



P bl



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Problem




2228-2240 (2011)


each time course

G ICA SOM



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Gene_ICA_SOM

JadeICA


SOM(20x20)


C Di t



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Centers=netiw11

Y=Centers

X=P


A=sum(X^22)ones(1M)

C=ones(N1)sum(Y^22)

B=XY

D=sqrt(A-2B+C)

Cross Distances

C Di t M t i




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




D 822x400


400 gene centers

400 clusters

Q



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Query



[xx ind]=min(D)


ind(i)

Vi li ti f d it





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course





for k=1M


end

a = linspace(-11K)

x = []for i=1K


x = [x xx]

end

y = num x=x

Fitting (x y)



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Fitting (xy)





Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course




Centers=netiw11

Y=Centers

a = linspace(-11K)

x = []

for i=1K


end

time = 1

y = Y( time) x=x

Problem



Problem






each time course

Problem



Problem





each time course



Problem






each time course

Problem



Problem





each time course



Problem





each time course

gene clustering

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