2005: a matlab tour on artificial immune systems
DESCRIPTION
BIC 2005 (Biologically Inspired Computing Conference), Johor, MalaysiaTRANSCRIPT
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A Matlab Tour on Some AIS A Matlab Tour on Some AIS AlgorithmsAlgorithms
BIC 2005: BIC 2005: International Symposium on Bio-Inspired ComputingInternational Symposium on Bio-Inspired Computing
Johor, MY, 10Johor, MY, 10thth September 2005 September 2005
Dr. Leandro Nunes de [email protected]
http://lsin.unisantos.b/lnunesCatholic University of Santos - UniSantos/Brazil
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BIC 2005 - A Matlab Tour on Some AIS - Dr. Leandro Nunes de Castro2
CLONALG: A Clonal Selection Algorithm
aiNet: An Artificial Immune Network
ABNET: An Antibody Network Opt-aiNet: An Optimization
Version of aiNet Discussion
Outline
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CLONALG
A Clonal Selection Algorithm
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BIC 2005 - A Matlab Tour on Some AIS - Dr. Leandro Nunes de Castro4
Increasing interest in biologically inspired systems
Systemic view of the immune system Main goals:
Provide a better understanding of the immune system
Solve engineering problems Study immune learning and memory
CLONALG
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Clonal Selection Principle
Proliferation(Cloning)
Differentiation
Plasma cells
Memory cellsSelection
Antigens
M
M
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Continuous Learning
Antigen A AntigensA + B
Primary Response SecondaryResponse
lag
Response toantigen A
Responseto antigen B
An
tibod
y co
nce
ntr
atio
n
Days
lag
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BIC 2005 - A Matlab Tour on Some AIS - Dr. Leandro Nunes de Castro7
Affinity Maturation
The cells that are most stimulated by the antigens suffer a hypermutation process single point, short deletions and sequence exchange
The hypermutation is proportional to antigenic affinity
The higher the cell affinity with the antigen, the greater its probability of being selected for differentiation and memory, thus surviving longer
The mutation rate is proportional to antigenic affinity
The editing process promotes a better exploration of the possible antigenic receptors
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Hypermutation Editing
Antigen-binding sites
Aff
inity A
A1
C1
C
B
B1
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CLONALG: Block Diagram
Maturate
Pr
M
Select
Clone
Pn
C
C*
(1)
(2)
(3)
(4)
(5)
Re-select
Nd
(6)
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1) Generate a set (P) of candidate solutions, composed of the subset of memory cells (M) added to the remaining (Pr) population (P = Pr + M)
2) Determine the n best individuals of the population (Pn), based on an affinity measure
3) Clone (reproduce) these n best individuals of the population, giving rise to a temporary population of clones (C). The clone size is an increasing function of the affinity with the antigen;
4) Submit the population of clones to a hypermutation scheme, where the hypermutation is proportional to the affinity of the antibody with the antigen. A maturated antibody population is generated (C*);
5) Re-select the improved individuals from C* to compose the memory set. Some members of the P set can be replaced by other improved members of C*;
6) Replace d low affinity antibodies of the population, maintaining its diversity.
CLONALG: Algorithm
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Test Problem I Pattern recognition (learning)
Cross-reactivity (generalization capability)
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Pattern Recognition (Learning)CLONALG - Performance I
00 generations
10 generations
20 generations
50 generations
75 generations
100 generations
150 generations
200 generations
250 generations
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Optimization function maximization
Test Problem II200 individuals
randomly distributed
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Multimodal Optimization (Maximization) Comparison with the Standard Genetic Algorithm (GA)
CLONALG - Performance II
GA
CLONALG
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Optimization Travelling Salesman Problem (TSP)
Test Problem III
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
7
1
8
14
2
15
3
4
1112
13
17
23
27 30
26
19
2124
29
2825
22
20
18
166
9
10
5
TSP
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
7
1
8
14
2
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3
4
1112
13
17
23
27 30
26
19
2124
29
2825
22
20
18
166
9
10
5
Cities Optimal Path (48872 um)
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Travelling Salesman (TSP) (Minimization)
CLONALG - Performance III
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
19
21
12
4
1127 30
26
24
29
28
205
10
22
257
1
8
14
2
3
15
6
9
16
18
13
17
23
TSP - 50 gen
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
10
5
7
1
8
14
2
15
3
1323
27 30
174
1112
6
9
16
19
26
24
29
2825
22
20
2118
TSP - 200 gen
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
1000
2000
3000
4000
5000
6000
7000
8000
9000
100004
1
15
20
6
11
28
16
18
26
27
22
24
25
102
199
7
21
30
3
8
17
13
14
23
29
5
12
TSP - 00 gen
0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
1
2
5
10
9
616
2313
1211
15
3
417
27 30
26
19
21
20
22
2528
29
24
18
7
8
14
TSP - 150 gen
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CLONALG: Discussion
General purpose algorithm inspired by the clonal selection and affinity maturation processes
Capabilities: learning and maintenance of high quality memory optimization
Crude version GA CSA:
same coding schemes different sources of inspiration related sequence of steps
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aiNet
An Artificial Immune Network
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Immune Network Theory
1
2
3
Ag
A ctiva tion
S upp res s ion
p1
i1
p2
i2
p3
i3
Ag(epitope)
Dynamics of the Immune System
Foreign stimulus
Internal image
Anti-idiotypic set
Recognizingset
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aiNet: Basic Principles (I) Definition:
The evolutionary artificial immune network, named aiNet, is an edge-weighted graph, not necessarily fully connected, composed of a set of nodes, called cells, and sets of node pairs called edges with a number assigned called weight, or connection strength, specified to each connected edge.
0.1 0.5
0.1 0.1
0.3 0.4
0.1
1 5 2
3 4 6
7
8 9
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Features: knowledge distributed among the cells competitive learning (unsupervised) constructive model with pruning phases generation and maintenance of diversity
Growing: clonal selection principle
Learning: directed affinity maturation
Pruning: natural death rate (low stimulated cells)
aiNet: Basic Principles (II)
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aiNet: Training Algorithm
At each generation: For each Ag
Affinity with the antigen (Ai) Agi-Ab
Clonal selection (n cells) Ai
Cloning Ai
Directed maturation (mutation) 1/Ai
Re-selection (%) Ai
Natural death (d) 1/Ai
Affinity between the network cells (Dii) Ab-Ab
Clonal suppression (s) Dii : (m - memory)
Mt [Mt;m]
Network suppression (s) Dii : (M Mt) M [M;meta]
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(affinity)
(clonal selection)
(directed
mutation)
(Re-selection)
(self discrimination)
(clonal suppression)
Stopping criterion: or fixed number of generations
L
iii AgAbA
1
2)(
kkkkk ),(μ AgAbAbAb
L
iii AbAbD
1
2)(
nkk kk ,...1 ,maxarg AbAg
%ζ,...,1 ,maxarg kk kk AbAg
kkk AbAb minarg
aiNet: Arithmetic
δA
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Test Problem I
Five Linearly Separable Classes
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 10
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
x
y
Training Patterns
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aiNet - Performance I
Minimal Spanning Tree
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
Number of Clusters (Valleys)
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
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0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
Final Network Structure
aiNet - Performance I
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2-Donuts: 500 samples
Test Problem II
-2-1
01
2
-2
0
2
4-1.5
-1
-0.5
0
0.5
1
1.5
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1
0 5 10 15 20 25 30 350
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Number of Clusters (Valleys)
Minimal Spanning Tree
aiNet - Performance II
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-1-0.5
00.5
1
-1
0
1
2
3-1
-0.5
0
0.5
1
1.5
Final Network Structure
aiNet - Performance II
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aiNet: Discussion
Iterative learning Robustness with low redundancy
(data compression) Clustering Related with neural networks User-defined parameters Gave rise to a number of other
algorithms
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ABNET
An Antibody Network
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ABNET
A single-layer feedforward neural network trained using ideas from the immune system
Constructive architecture with pruning phases
Boolean weights
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ABNET: Basic Functioning (I)
Ab population
Ab re-selection
Clone Death
Affinity maturation
Most stimulated cell Non-stimulated cell
Ab selection
Antigenic stimuli
Neurons (k)
Competition
Split Prune
Weightupdate
Winner Inactive neuron
Input patterns
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Affinity measure (Hamming distance):
Main loop of the algorithm Choose randomly an antigen (pattern) Determine the cell Abk with highest affinity Update the weight vector of this cell Increase the concentration level (j) of this
cell Attribute va = k
kkk AbAg maxarg
ABNET: Basic Functioning (I)
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ABNET: Growing
}1τ|{ where, maxarg
jjjOj
Os AbAb
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ABNET: Pruning
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ABNET: Weight Update
1 0 0 0 1 0 1 1
0 0 1 1 1 1 1 0
0 1 1 1 1 1 1 0
Ag
Abk (Affinity: 5)
Ag
Abk (Affinity: 6)
1 0 0 0 1 0 1 1
Updating ( = 1)
1 0 0 0 1 0 1 1
0 0 1 1 1 1 1 0
0 1 1 1 0 1 1 0
Ag
Abk (Affinity: 5)
Ag
Abk (Affinity: 7)
1 0 0 0 1 0 1 1
Updating ( = 2)
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01
23
45
0.4
0.3
0.2
0.1
020
40
60
80
100
Noise Tolerance - ABNET
Noise level
Cla
ssifi
catio
n (%
)
ABNET - Performance2) Cross-reactivity
(generalization)
(a) 13.75%
Noise tolerance:
(b) 13.75%
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ABNET: Discussion
Performs clustering (data reduction) Easily implemented in hardware Robust to solve binary tasks Adapted to solve real-valued problems,
both clustering and classification
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Opt-aiNet
An Optimization version of aiNet
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Introduction
The algorithm for opt-aiNet is an adaptation of a discrete artificial immune network usually applied in data analysis
Features of opt-aiNet: population size dynamically adjustable exploitation and exploration of the search-
space capability of locating multiple optima automatic stopping criterion
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Immune Networks
N. Jerne suggested that immune cells and molecules present antigenic peptides
p1
i1
p2
i2
p3
i3
Ag(epitope)
Molecular interactions in the immune system
Foreign stimulus
Internal image
Anti-idiotypic set
Recognizing set
i1
px
Non-specific set
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opt-aiNet
1. Randomly initialize a population of cells (initial number not relevant)
2. While not [constant memory population], do2.1Calculate the fitness and normalize the vector of fitnesses.2.2Generate a number Nc of clones for each network cell.2.3Mutate each clone proportionally to the fitness of its parent cell, but
keep the parent cell.2.4Determine the fitness of all individuals of the population.2.5For each clone, select the cell with highest fitness and calculate the
average fitness of the selected population.2.6 If the average fitness of the population is not significantly
different from the previous iteration, then continue. Else, return to step 2.1
2.7Determine the affinity of all cells in the network. Suppress all but the highest fitness of those cells whose affinities are less than the suppression threshold s and determine the number of network cells, named memory cells, after suppression.
2.8Introduce a percentage d% of randomly generated cells and return to step 2.
3. EndWhile
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Related Strategies
CLONALG: encoding, static population size, no inter-
cell interaction, different mutation scheme Evolution Strategies
equal to ( + )-ES, where = N and = Nc; both use Gaussian mutation, but with different standard deviations, static population size, no diversity introduction, no direct interaction within the population
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Simulation Results (I)
Multi Function
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Simulation Results (II)
Roots Function
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Simulation Results (III)
Schaffer’s Function
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Opt-aiNet: Discussion
The algorithm is an adaptation of an immune network model designed to perform data analysis
Features: Exploration and exploitation of the search-
space Double-plastic search Automatic convergence criteria
Adapted to solve combinatorial and dynamic optimization
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Final Comments
Biological Inspiration utility and extension improved comprehension of natural phenomena
Example based learning, where different pattern categories are represented by adaptive memories of the system
An iterative artificial immune network
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CLONALG high degree of parallelism by controlling the hipermutation rate an
initial search for most general characteristics can be performed, followed by the search for smaller details
trade off between the clone size and the convergence speed
possibility of using heuristics to obtain global optima for problems like TSP
Final Comments
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aiNet Models continuous spaces without the need of
integration Iterative model dynamic models (DE) Robustness with low redundancy Clustering without a direct measure of
distance* RNA: knowledge distributed along the
connections aiNet: knowledge distributed in the cells large amount of user defined parameters Specific cells general cells
ABNET clustering, or grouping of similar patterns capability of solving binary tasks
Final Comments
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Final Comments
Opt-aiNet ;lsdkasdkj