Cellular Automata Machine For Pattern Recognition Pradipta Maji 1 Niloy Ganguly 2 Sourav Saha 1 Anup K Roy 1 P Pal Chaudhuri 1 1 Department of Computer.

Cellular Automata Machine For Pattern Recognition

Pradipta Maji1 Niloy Ganguly 2

Sourav Saha1 Anup K Roy1 P Pal Chaudhuri 1

1 Department of Computer Science & Technology , Bengal Engineering College ( D . U ) , Howrah ,

West Bengal , India 711103

2Department of Business Administration , Indian Institute of Social Welfare and Business Management , Calcutta ,

West Bengal , India 700073

CA Research Group (BECDU)

The Problem• Pattern Recognition - Study how

machines can learn to distinguish patterns of interest

• Conventional Approach - Compares input patterns with each of the stored patterns learn

A

B

C …

Z

Bookman Old StyleA

Comic Sans MS



The Problem

A

Comic Sans MS

A A BA

B

C …

Z

Bookman

old Style

Grid by Grid Comparison



The Problem

A A BGrid by Grid Comparison

0 0 1 00 0 1 00 1 1 11 0 0 11 0 0 1

0 1 1 00 1 1 00 1 1 01 0 0 11 0 0 1

No of Mismatch = 3



The Problem

A A BGrid by Grid Comparison

0 0 1 00 0 1 00 1 1 11 0 0 11 0 0 1

1 1 1 00 1 0 10 1 1 10 1 0 11 1 1 0

No of Mismatch = 9



The Problem• Time to recognize a pattern -

Proportional to the number of stored patterns ( Too costly with the increase of number of patterns stored )

Solution - Associative Memory Modeling



The Problem• Time to recognize a pattern -

Proportional to the number of stored patterns ( Too costly with the increase of number of patterns stored )

Solution - Associative Memory Modeling

A

B

C


Transient

A

AA

AA

A

Transient

Transient


Associative Memory• Entire state space - Divided into some

pivotal points.• State close to pivot - Associated with

that pivot.• Time to recognize pattern-Independent

of number of stored patterns.

A

B

CTransient

A

AA

AA

A

Transient

Transient



Associative MemoryTwo Phase : Learning and DetectionTime to learn is higherDriving a car Difficult to learn but once learnt it

becomes natural

A

B

CTransient

A

AA

AA

A

Transient

Transient



Associative Memory (Hopfield Net)

Densely connected Network - Problems to implement in Hardware

• Solution - Cellular Automata (Sparsely connected machine) - Ideally suitable for VLSI application

A

B

CTransient

A

AA

AA

A

Transient

Transient



Cellular Automata

VLSI Domain • India under Prof. P Pal Chaudhuri• Late 80’s - Work at Indian

Institute of Technology Kharagpur• Late 90’s - Work at Bengal

Engineering College Deemed University, Calcutta

Book - Additive Cellular Automata Vol I, IEEE Press



Cellular Automata A computational Model with discrete

cells updated synchronously

………..

outputInput

Combinational Logic

Clock

From Left Neighbor

From Right Neighbor

0/1

2 - State 3-Neighborhood CA Cell



Cellular AutomataCombinational Logic can be of 256 typeseach type is called a rule

Each cell can have 256 different rules

………..


98 236 226 107

4 cell CA with different rules at each cell


State Transition Diagram

1

21163 135

12 15 14 4 810 7

9

0

9 15

613

7 12

3 14

11

5

2 8

1 4

10

0



Generalized Multiple Attractor CA

A

B

CTransient

A

AA

AA

A

Transient

Transient

The State Space of GMACA – Models an Associative Memory0100 1000

1010 0001

0101

0011

0010

0000

11010111

1100 1001

10110110

1110

1111

P1 attractor-1

P2 atractor-2

Rule vector:<202,168,218,42>



Generalized Multiple Attractor CA

0100 1000

1010 0001

0101

0011

0010

0000

11010111

1100 1001

10110110

1110

1111

P1 attractor-1

P2 atractor-2

Rule vector:<202,168,218,42>


Pivot PointsPivot Points

Dist =3

Dist =1

The state transition diagram breaks into disjoint attractor basin Each attractor basin of CA should contain one and only one pattern to be learnt in its attractor cycle The hamming distance of each state with its attractor is less than that of other attractors.


Synthesis of GMACA Reverse Engineering Technique Phase I: Random Generation of a set of directed Graph

Basin 1

0100 1000

0001

0010 0000

1110 11011011

0111

1111

Basin 2

Patterns to be learnt P1 = 0000 P2 = 1111

Number of bits of noise = 1


1

0


Synthesis of GMACA Reverse Engineering Technique

Phase II: State transition table from Graph

Basin 1

0100 1000

0001

0010 0000


PresentState

NextState

01001000001000010000

00010001000100000010


Synthesis of GMACA Reverse Engineering Technique

Phase II: State transition table from Graph


PresentState

NextState

11101011110101111111

01110111011111111111

1110 11011011

0111

1111

Basin 2


Synthesis of GMACA Reverse Engineering TechniquePhase III: GMACA rule vector from State transition table


PresentState

NextState

11101011110101111111

01110111011111111111

PresentState

NextState

01001000001000010000

00010001000100000010

Basin 1 Basin 2




Basin 1 Basin 2PrestState

NextState

010100001000000

00000

PrestState

NextState

111101110011111

11111

NEIGHBORHOODSTATE

111 110 101 100 011 010 001 000

Next State




Basin 1 Basin 2PrestState

NextState

010100001000000

00000

PrestState

NextState

111101110011111

11111

NEIGHBORHOODSTATE

111 110 101 100 011 010 001 000

Next State

111 1

111 1

1

000 0

000 0

01

101 1

0

010 0

1

110 1

0

001 0

1

011 1

0

100 0

Rule 232




PresentState

NextState

11101011110101111111

01110111011111111111

PresentState

NextState

01001000001000010000

00010001000100000010

Basin 1 Basin 2

NEIGHBORHOODSTATE

111 110 101 100 011 010 001 000

Next State

000 0

000 1

0/1?Collision




NEIGHBORHOODSTATE

111 110 101 100 011 010 001 000

Next State0/1?Collision

Less the number of collision better the design.

Design Objective :

Design GMACA so that there is minimum number of collision during rule formation

Simulated Annealing to attain the design

•


Objective Reduce Collision Increment of Cycle Length

Simulated Annealing Program Mutation Technique - 1

1110 1101 0111

1011

1111

Cycle Length = 2

1110 1101 0111

1111

Cycle Length = 1

1011

•


Simulated Annealing Program Increment of Cycle Length

Present State

Next State

1110 1101 0111 1011 1111

1011 1011 1011 1111 1111

111 1

111 0

NEIGHBORHOOD STATE

111 110 101 100 011 010 001 000

Next State

*1 *0 *0*0/1?

1110 1101 0111

1111

Cycle Length = 1

1011

•


Simulated Annealing Program Increment of Cycle Length

Present State

Next State

1110 1101 0111 1011 1111

1011 1011 1011 1111 1011

NEIGHBORHOOD STATE

111 110 101 100 011 010 001 000

Next State

Next State

*1 *0 *0*0/1?

111 0

111 0

1110 1101 0111

1011

1111

Cycle Length = 2

0 *1 *0 *0*

•


Reduction of Cycle Length

Simulated Annealing Program Mutation Technique - 2

Cycle Length = 4

1110 1101 1011

01111111

Cycle Length = 3

1110 1101 1011

01111111

•


Simulated Annealing Program Decrement of Cycle Length

PresentState

NextState

11101101101101111111

11011101011111111101111 0

111 1

NEIGHBORHOOD STATE

111 110 101 100 011 010 001 000

Next State

0/1? *0 *0 *1*

Cycle Length = 4

1110 1101 1011

01111111

•


Simulated Annealing Program Decrement of Cycle LengthNEIGHBORHOOD STATE

111 110 101 100 011 010 001 000

Next State

Next State

*1 *0 *0*0/1?

PresentState

NextState

11101101101101111111

11011101011111111011111 1

111 1

1 *1 *0 *0*

Cycle Length = 3

1110 1101 1011

01111111

•


• Memorizing Capacity

• Evolution Time

• Identification / Recognition Complexity

Performance of GMACA Based Pattern Recognizer

•


Memorizing Capacity

Pattern Length

GMACA Hopfield Net

20 5 3 40 10 6 60 13 9 80 18 12 100 23 15

Conclusion : GMACA have much higher capacity than Hopfield Net

•


Evolution Time

Pattern N o ofPatterns

In itialTem p

EvolutionTim e(m in)

20 5 15 1.06

40 10 20 3.01

60 13 25 4.52

80 18 35 7.45

100 23 40 15.08

•


Identification / Recognition Complexity

• Cost of Computation for Recognition / Identification - Constant


Achievements

1.Cellular Automata - A powerful machine in designing the pattern recognition tool

2.Storage Capacity of CA - Higher than Hopfield Net

3.A clever reverse engineering technique is employed to design Cellular Automata based Associative Memory


PublicationsStudy of Non-Linear Cellular Automata For Pattern

Recognition To be published in IEEE Transaction, Man, Machine and Cybernetics, Part - B

Generalized Multiple Attractor Cellular Automata(GMACA) Model for Associative Memory Niloy Ganguly, Pradipta Maji, Biplab k Sikdar and P Pal Chaudhuri To be published in International Journal for Pattern Recognition and Artificial Intelligence

Error Correcting Capability of Cellular Automata Based Associative Memory, IEEE Transaction, Man, Machine and Cybernetics, Part - A

Thank you

Niloy Ganguly

[email protected]

http://ppc.becs.ac.in

Cellular Automata Machine For Pattern Recognition Pradipta Maji 1 Niloy Ganguly 2 Sourav Saha 1 Anup K Roy 1 P Pal Chaudhuri 1 1 Department of Computer.

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