agglomerative hierarchical clustering - computer science · 2010. 11. 2. · agglomerative...

AgglomerativeHierarchicalClustering

10/14/20101

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Agglomerative Hierarchical Clustering

James Loomis & Paul Romanczyk

October 27, 2010


10/14/20102

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Outline

Outline

Introduction

Distance

ExampleSingle Linkage Distance MatricesCluster PlotsDendrogramsSummary

References

Questions

Extra StuffTotal Linkage Distance MatricesAverage Linkage Distance Matrices


10/14/20103

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Hierarchical ClusteringHierarchical clustering:

I Clustering using a hierarchy of clusters

I May be represented in a tree structure (dendrogram)

I Root - a single cluster containing all observations

I Leaves - individual observations.

x1

x8

x7

x6

x5

x4

x3

x2


10/14/20104

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Dendrogram

[Duda et al., 2001] Figure 10.11


10/14/20105

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Two Distinct Approaches:

I Agglomerative (bottom up, clumping)I Start with n singleton clustersI Successively merge (”clump”) clustersI Computation from one level to another generally simplerI For small number of clusters, takes many iterations

I Divisive (top down, splitting)I Start with one clusterI Successively split clustersI Single iteration is more expensiveI With fewer clusters, fewer iterations


10/14/20105

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Two Distinct Approaches:I Agglomerative (bottom up, clumping)

I Start with n singleton clustersI Successively merge (”clump”) clustersI Computation from one level to another generally simplerI For small number of clusters, takes many iterations

I Divisive (top down, splitting)I Start with one clusterI Successively split clustersI Single iteration is more expensiveI With fewer clusters, fewer iterations


10/14/20106

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Agglomerative Clustering Algorithm

1 c , ĉ ← n2 Di ← {xi} where i = 1, . . . , n

3 do ĉ ← ĉ − 14 find nearest clusters Di , Dj5 merge Di and Dj6 until c = ĉ

7 return c clusters

How do we determine which two clusters are nearest?


10/14/20107

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Properties of Distance

I Distance is non-negative.I D(x , y) ≥ 0

I D(x , y) = 0 if and only if x = y .I Distance is symmetric.

I D(x , y) = D(y , x)

I Distance satisfies the triangle inequalityI D(x , z) ≤ D(x , y) + D(y , z)


10/14/20108

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Distance Measures—Between Points

Let ~x1 = [ x1,1 x1,2 · · · x1,n ]T and~x2 = [ x2,1 x2,2 · · · x2,n ]T

Name Formula

Manhattan d1(~x1, ~x2) =∑n

i=1 |x1,i − x2,i |Euclidian d2(~x1, ~x2) =

√∑ni=1 |x1,i − x2,i |

2

P-norm dp(~x1, ~x2) =p√∑n

i=1 |x1,i − x2,i |p

Statistical ds(~x1, ~x2) =

√∑ni=1

(x1,i−x2,i

σi

)2Mahalanobis dm(~x1, ~x2) =

√(~x1 − ~µ)Σ−1(~x2 − ~µ)T

Cosine dc(~x1, ~x2) =~x1

T ~x1||~x2||·||~x2||

Chebyshev dC (~x1, ~x2) = max(|x1,i − x2,i |)


10/14/20109

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Distance Measures—Between Clusters

Single Linkage d(U,V ),W = min{dU,W , dV ,W }

d2,4

1

2

3

4 5

Complete Linkage d(U,V ),W = max{dU,W , dV ,W }

d1,5

1

2

3

4 5

Average Linkage d(U,V ),W =

∑i

∑j

di ,j

NU,V NW2∑

i=1

5∑j=3

di ,j

2·3

1

2

3

4 5


10/14/201010

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Data

x y

-1.3508 0.9010-0.3674 1.1548-1.5895 -0.0732-1.3615 0.1443-0.7088 0.33240.3155 -0.32201.6638 0.25670.4751 0.25822.0778 0.28481.3015 -1.0126


10/14/201011

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 11 2 3 4 5 6 7 8 9 10

1 0.00 1.02 1.00 0.76 0.86 2.07 3.08 1.94 3.48 3.272 1.02 0.00 1.73 1.42 0.89 1.63 2.22 1.23 2.60 2.743 1.00 1.73 0.00 0.32 0.97 1.92 3.27 2.09 3.68 3.044 0.76 1.42 0.32 0.00 0.68 1.74 3.03 1.84 3.44 2.905 0.86 0.89 0.97 0.68 0.00 1.22 2.37 1.19 2.79 2.426 2.07 1.63 1.92 1.74 1.22 0.00 1.47 0.60 1.86 1.207 3.08 2.22 3.27 3.03 2.37 1.47 0.00 1.19 0.41 1.328 1.94 1.23 2.09 1.84 1.19 0.60 1.19 0.00 1.60 1.529 3.48 2.60 3.68 3.44 2.79 1.86 0.41 1.60 0.00 1.51

10 3.27 2.74 3.04 2.90 2.42 1.20 1.32 1.52 1.51 0.00


10/14/201012

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 21 2 5 6 7 8 9 10 11

1 0.00 1.02 0.86 2.07 3.08 1.94 3.48 3.27 0.762 1.02 0.00 0.89 1.63 2.22 1.23 2.60 2.74 1.425 0.86 0.89 0.00 1.22 2.37 1.19 2.79 2.42 0.686 2.07 1.63 1.22 0.00 1.47 0.60 1.86 1.20 1.747 3.08 2.22 2.37 1.47 0.00 1.19 0.41 1.32 3.038 1.94 1.23 1.19 0.60 1.19 0.00 1.60 1.52 1.849 3.48 2.60 2.79 1.86 0.41 1.60 0.00 1.51 3.44

10 3.27 2.74 2.42 1.20 1.32 1.52 1.51 0.00 2.9011 0.76 1.42 0.68 1.74 3.03 1.84 3.44 2.90 0.00


10/14/201013

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 31 2 5 6 8 10 11 12

1 0.00 1.02 0.86 2.07 1.94 3.27 0.76 3.082 1.02 0.00 0.89 1.63 1.23 2.74 1.42 2.225 0.86 0.89 0.00 1.22 1.19 2.42 0.68 2.376 2.07 1.63 1.22 0.00 0.60 1.20 1.74 1.478 1.94 1.23 1.19 0.60 0.00 1.52 1.84 1.19

10 3.27 2.74 2.42 1.20 1.52 0.00 2.90 1.3211 0.76 1.42 0.68 1.74 1.84 2.90 0.00 3.0312 3.08 2.22 2.37 1.47 1.19 1.32 3.03 0.00


10/14/201014

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 41 2 5 10 11 12 13

1 0.00 1.02 0.86 3.27 0.76 3.08 1.942 1.02 0.00 0.89 2.74 1.42 2.22 1.235 0.86 0.89 0.00 2.42 0.68 2.37 1.19

10 3.27 2.74 2.42 0.00 2.90 1.32 1.2011 0.76 1.42 0.68 2.90 0.00 3.03 1.7412 3.08 2.22 2.37 1.32 3.03 0.00 1.1913 1.94 1.23 1.19 1.20 1.74 1.19 0.00


10/14/201015

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 51 2 10 12 13 14

1 0.00 1.02 3.27 3.08 1.94 0.762 1.02 0.00 2.74 2.22 1.23 0.89

10 3.27 2.74 0.00 1.32 1.20 2.4212 3.08 2.22 1.32 0.00 1.19 2.3713 1.94 1.23 1.20 1.19 0.00 1.1914 0.76 0.89 2.42 2.37 1.19 0.00


10/14/201016

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 62 10 12 13 15

2 0.00 2.74 2.22 1.23 0.8910 2.74 0.00 1.32 1.20 2.4212 2.22 1.32 0.00 1.19 2.3713 1.23 1.20 1.19 0.00 1.1915 0.89 2.42 2.37 1.19 0.00


10/14/201017

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 710 12 13 16

10 0.00 1.32 1.20 2.4212 1.32 0.00 1.19 2.2213 1.20 1.19 0.00 1.1916 2.42 2.22 1.19 0.00


10/14/201018

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 810 12 17

10 0.00 1.32 1.2012 1.32 0.00 1.1917 1.20 1.19 0.00


10/14/201019

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using single linkage. Iteration: 910 18

10 0.00 1.2018 1.20 0.00


10/14/201020

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example–Linkage Step 1

−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10

Single Linkage Complete Linkage Average Linkage


10/14/201021

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201022

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201023

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201024

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201025

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201026

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201027

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201028

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201029

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


−2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5−1.5

−1

−0.5

0

0.5

1

1.5

1

2

3

4

5

6

7 8 9

10



10/14/201030

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example–Dendrogram

1 2 3 5 7 10 8 6 9 4

0.5

0.6

0.7

0.8

0.9

1

1.1

Class

Dis

tance


10/14/201031

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


1 2 3 5 4 7 10 6 9 8

0.5

1

1.5

2

2.5

3

3.5

Class

Dis

tance


10/14/201032

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


1 2 3 7 10 4 5 6 9 8

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

Class

Dis

tance


10/14/201033

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices


1 2 3 5 7 10 8 6 9 40

0.5

1

1.5

2

2.5

3

3.5

Class

Distan

ce

1 2 3 5 4 7 10 6 9 80

0.5

1

1.5

2

2.5

3

3.5

Class

Distan

ce

1 2 3 7 10 4 5 6 9 80

0.5

1

1.5

2

2.5

3

3.5

Class

Distan

ce



10/14/201034

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Single Linkage Complete Linkage Average Linkagedist. action dist. action dist. action

0.3151 {4, 3} → 11 0.3151 {4, 3} → 11 0.3151 {4, 3} → 110.4149 {9, 7} → 12 0.4149 {9, 7} → 12 0.4149 {9, 7} → 120.6018 {8, 6} → 13 0.6018 {8, 6} → 13 0.6018 {8, 6} → 130.6792 {11, 5} → 14 0.8576 {5, 1} → 14 0.8244 {11, 5} → 140.7568 {14, 1} → 15 1.0030 {14, 11} → 15 0.8724 {14, 1} → 150.8904 {15, 2} → 16 1.5119 {12, 10} → 16 1.2640 {15, 2} → 161.1862 {16, 13} → 17 1.6271 {13, 2} → 17 1.3598 {13, 10} → 171.1887 {17, 12} → 18 2.0910 {17, 15} → 18 1.4924 {17, 12} → 181.2038 {10, 18} → 19 3.2706 {16, 18} → 19 2.4476 {16, 18} → 19


10/14/201035

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

References

Duda, R., Hart, P., and Stork, D. (2001).Pattern Classification.John Wiley and Sons, 2nd edition.

Johnson, R. and Wichern, D. (2007).Applied multivariate statistical data analysis.Prentice Hall: Upper Saddle River, NJ, 6th edition.


10/14/201036

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Questions


10/14/201037

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 11 2 3 4 5 6 7 8 9 10

1 0.00 1.02 1.00 0.76 0.86 2.07 3.08 1.94 3.48 3.272 1.02 0.00 1.73 1.42 0.89 1.63 2.22 1.23 2.60 2.743 1.00 1.73 0.00 0.32 0.97 1.92 3.27 2.09 3.68 3.044 0.76 1.42 0.32 0.00 0.68 1.74 3.03 1.84 3.44 2.905 0.86 0.89 0.97 0.68 0.00 1.22 2.37 1.19 2.79 2.426 2.07 1.63 1.92 1.74 1.22 0.00 1.47 0.60 1.86 1.207 3.08 2.22 3.27 3.03 2.37 1.47 0.00 1.19 0.41 1.328 1.94 1.23 2.09 1.84 1.19 0.60 1.19 0.00 1.60 1.529 3.48 2.60 3.68 3.44 2.79 1.86 0.41 1.60 0.00 1.51

10 3.27 2.74 3.04 2.90 2.42 1.20 1.32 1.52 1.51 0.00


10/14/201038

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 21 2 5 6 7 8 9 10 11

1 0.00 1.02 0.86 2.07 3.08 1.94 3.48 3.27 1.002 1.02 0.00 0.89 1.63 2.22 1.23 2.60 2.74 1.735 0.86 0.89 0.00 1.22 2.37 1.19 2.79 2.42 0.976 2.07 1.63 1.22 0.00 1.47 0.60 1.86 1.20 1.927 3.08 2.22 2.37 1.47 0.00 1.19 0.41 1.32 3.278 1.94 1.23 1.19 0.60 1.19 0.00 1.60 1.52 2.099 3.48 2.60 2.79 1.86 0.41 1.60 0.00 1.51 3.68

10 3.27 2.74 2.42 1.20 1.32 1.52 1.51 0.00 3.0411 1.00 1.73 0.97 1.92 3.27 2.09 3.68 3.04 0.32


10/14/201039

Loomis &Romanczyk

Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 31 2 5 6 8 10 11 12

1 0.00 1.02 0.86 2.07 1.94 3.27 1.00 3.482 1.02 0.00 0.89 1.63 1.23 2.74 1.73 2.605 0.86 0.89 0.00 1.22 1.19 2.42 0.97 2.796 2.07 1.63 1.22 0.00 0.60 1.20 1.92 1.868 1.94 1.23 1.19 0.60 0.00 1.52 2.09 1.60

10 3.27 2.74 2.42 1.20 1.52 0.00 3.04 1.5111 1.00 1.73 0.97 1.92 2.09 3.04 0.32 3.6812 3.48 2.60 2.79 1.86 1.60 1.51 3.68 0.41


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 41 2 5 10 11 12 13

1 0.00 1.02 0.86 3.27 1.00 3.48 2.072 1.02 0.00 0.89 2.74 1.73 2.60 1.635 0.86 0.89 0.00 2.42 0.97 2.79 1.22

10 3.27 2.74 2.42 0.00 3.04 1.51 1.5211 1.00 1.73 0.97 3.04 0.32 3.68 2.0912 3.48 2.60 2.79 1.51 3.68 0.41 1.8613 2.07 1.63 1.22 1.52 2.09 1.86 0.60


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 52 10 11 12 13 14

2 0.00 2.74 1.73 2.60 1.63 1.0210 2.74 0.00 3.04 1.51 1.52 3.2711 1.73 3.04 0.32 3.68 2.09 1.0012 2.60 1.51 3.68 0.41 1.86 3.4813 1.63 1.52 2.09 1.86 0.60 2.0714 1.02 3.27 1.00 3.48 2.07 0.86


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 62 10 12 13 15

2 0.00 2.74 2.60 1.63 1.7310 2.74 0.00 1.51 1.52 3.2712 2.60 1.51 0.41 1.86 3.6813 1.63 1.52 1.86 0.60 2.0915 1.73 3.27 3.68 2.09 1.00


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 72 13 15 16

2 0.00 1.63 1.73 2.7413 1.63 0.60 2.09 1.8615 1.73 2.09 1.00 3.6816 2.74 1.86 3.68 1.51


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 815 16 17

15 1.00 3.68 2.0916 3.68 1.51 2.7417 2.09 2.74 1.63


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using total linkage. Iteration: 916 18

16 0.00 3.2718 3.27 0.00


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 11 2 3 4 5 6 7 8 9 10

1 0.00 1.02 1.00 0.76 0.86 2.07 3.08 1.94 3.48 3.272 1.02 0.00 1.73 1.42 0.89 1.63 2.22 1.23 2.60 2.743 1.00 1.73 0.00 0.32 0.97 1.92 3.27 2.09 3.68 3.044 0.76 1.42 0.32 0.00 0.68 1.74 3.03 1.84 3.44 2.905 0.86 0.89 0.97 0.68 0.00 1.22 2.37 1.19 2.79 2.426 2.07 1.63 1.92 1.74 1.22 0.00 1.47 0.60 1.86 1.207 3.08 2.22 3.27 3.03 2.37 1.47 0.00 1.19 0.41 1.328 1.94 1.23 2.09 1.84 1.19 0.60 1.19 0.00 1.60 1.529 3.48 2.60 3.68 3.44 2.79 1.86 0.41 1.60 0.00 1.51

10 3.27 2.74 3.04 2.90 2.42 1.20 1.32 1.52 1.51 0.00


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 21 2 5 6 7 8 9 10 11

1 0.00 1.02 0.86 2.07 3.08 1.94 3.48 3.27 0.882 1.02 0.00 0.89 1.63 2.22 1.23 2.60 2.74 1.585 0.86 0.89 0.00 1.22 2.37 1.19 2.79 2.42 0.826 2.07 1.63 1.22 0.00 1.47 0.60 1.86 1.20 1.837 3.08 2.22 2.37 1.47 0.00 1.19 0.41 1.32 3.158 1.94 1.23 1.19 0.60 1.19 0.00 1.60 1.52 1.979 3.48 2.60 2.79 1.86 0.41 1.60 0.00 1.51 3.56

10 3.27 2.74 2.42 1.20 1.32 1.52 1.51 0.00 2.9711 0.88 1.58 0.82 1.83 3.15 1.97 3.56 2.97 0.16


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 31 2 5 6 8 10 11 12

1 0.00 1.02 0.86 2.07 1.94 3.27 0.88 3.282 1.02 0.00 0.89 1.63 1.23 2.74 1.58 2.415 0.86 0.89 0.00 1.22 1.19 2.42 0.82 2.586 2.07 1.63 1.22 0.00 0.60 1.20 1.83 1.678 1.94 1.23 1.19 0.60 0.00 1.52 1.97 1.40

10 3.27 2.74 2.42 1.20 1.52 0.00 2.97 1.4211 0.88 1.58 0.82 1.83 1.97 2.97 0.16 3.3612 3.28 2.41 2.58 1.67 1.40 1.42 3.36 0.21


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 41 2 5 10 11 12 13

1 0.00 1.02 0.86 3.27 0.88 3.28 2.002 1.02 0.00 0.89 2.74 1.58 2.41 1.435 0.86 0.89 0.00 2.42 0.82 2.58 1.20

10 3.27 2.74 2.42 0.00 2.97 1.42 1.3611 0.88 1.58 0.82 2.97 0.16 3.36 1.9012 3.28 2.41 2.58 1.42 3.36 0.21 1.5313 2.00 1.43 1.20 1.36 1.90 1.53 0.30


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 51 2 10 12 13 14

1 0.00 1.02 3.27 3.28 2.00 0.872 1.02 0.00 2.74 2.41 1.43 1.35

10 3.27 2.74 0.00 1.42 1.36 2.7912 3.28 2.41 1.42 0.21 1.53 3.1013 2.00 1.43 1.36 1.53 0.30 1.6714 0.87 1.35 2.79 3.10 1.67 0.44


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 62 10 12 13 15

2 0.00 2.74 2.41 1.43 1.2610 2.74 0.00 1.42 1.36 2.9112 2.41 1.42 0.21 1.53 3.1413 1.43 1.36 1.53 0.30 1.7515 1.26 2.91 3.14 1.75 0.57


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 710 12 13 16

10 0.00 1.42 1.36 2.8712 1.42 0.21 1.53 3.0013 1.36 1.53 0.30 1.6916 2.87 3.00 1.69 0.77


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 812 16 17

12 0.21 3.00 1.4916 3.00 0.77 2.0817 1.49 2.08 0.74


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Outline

Introduction

Distance

Example

S.L. Dist. Matrices

Cluster Plots

Dendrodgrams

Summary

References

Questions

Extra Stuff

T.L. Dist. Matrices

A.L. Dist. Matrices

Example

Cluster distances using average linkage. Iteration: 916 18

16 0.00 2.4518 2.45 0.00

OutlineIntroductionDistanceExampleSingle Linkage Distance MatricesCluster PlotsDendrogramsSummary

ReferencesQuestionsExtra StuffTotal Linkage Distance MatricesAverage Linkage Distance Matrices

agglomerative hierarchical clustering - computer science · 2010. 11. 2. · agglomerative...

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