2005: A Matlab Tour on Artificial Immune Systems

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

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

CLONALG

A Clonal Selection Algorithm


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


Clonal Selection Principle

Proliferation(Cloning)

Differentiation

Plasma cells

Memory cellsSelection

Antigens

M

M


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


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


Hypermutation Editing

Antigen-binding sites

Aff

inity A

A1

C1

C

B

B1


CLONALG: Block Diagram

Maturate

Pr

M

Select

Clone

Pn

C

C*

(1)

(2)

(3)

(4)

(5)

Re-select

Nd

(6)


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


Test Problem I Pattern recognition (learning)

Cross-reactivity (generalization capability)


Pattern Recognition (Learning)CLONALG - Performance I

00 generations

10 generations

20 generations

50 generations

75 generations

100 generations

150 generations

200 generations

250 generations


Optimization function maximization

Test Problem II200 individuals

randomly distributed


Multimodal Optimization (Maximization) Comparison with the Standard Genetic Algorithm (GA)

CLONALG - Performance II

GA

CLONALG


Optimization Travelling Salesman Problem (TSP)

Test Problem III

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

1000

2000

3000

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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

15

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)


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

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24

25

102

199

7

21

30

3

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14

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29

5

12

TSP - 00 gen

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

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2000

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5000

6000

7000

8000

9000

10000

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2

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10

9

616

2313

1211

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3

417

27 30

26

19

21

20

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2528

29

24

18

7

8

14

TSP - 150 gen


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

aiNet

An Artificial Immune Network


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


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


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)


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]


(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


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


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


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


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


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


-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


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

ABNET

An Antibody Network


ABNET

A single-layer feedforward neural network trained using ideas from the immune system

Constructive architecture with pruning phases

Boolean weights


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


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)


ABNET: Growing

}1τ|{ where, maxarg

jjjOj

Os AbAb


ABNET: Pruning


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)


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%


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

Opt-aiNet

An Optimization version of aiNet


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


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


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


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


Simulation Results (I)

Multi Function


Simulation Results (II)

Roots Function


Simulation Results (III)

Schaffer’s Function


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


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


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


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


Final Comments

Opt-aiNet ;lsdkasdkj

[email protected]

Questions? Comments?

2005: A Matlab Tour on Artificial Immune Systems

Technology

affinity clonal selection

antigenic affinity

memory clonalg

ag affinity

affinity measure

cell affinity

network cells d

antibody network