Pattern Recognition in Soft Computing

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Pattern Recognition in Soft Computing
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Soft Computing

• Computing paradigm (consortium of complementary
  methodologies) that is tolerant of imprecision,
  uncertainty, partial truth,near-optimality
• Goal is to achieve robustness, tractability and
  low cost solution.

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Fuzzy Logic
Approximate reasoning
Neural Networks
Soft Computing
Chaos Theory
Genetic Algorithms
Rough Sets
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GENETIC ALGORITHMS

• DEFINITION
• Randomized search and optimization technique
  guided by the principle of natural genetic
  systems.
• Why Genetic Algorithms (GAs) ?
• Many real life problems cannot be solved in
  polynomial amount of time using deterministic
  algorithm
• Sometimes near optimal solutions that can be
  generated quickly are more desirable than optimal
  solutions which require huge amount of time
• Problems can be modeled as an optimization one.

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Search TechniquesThe traditional vs. the
unconventional

• Calculus based techniques gradient descent
• (hill climbing)

local optima
Global optima
Continuous domain, quadratic optimization best
method
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Search TechniquesThe traditional vs. the
unconventional

• Enumerative technique dynamic
• programming

n points
What if n very very large? Quite likely in
practice.
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Search TechniquesThe traditional vs. the
unconventional

• Random technique hoping to find the optimal
• sooner.

No better than enumerative in the long run
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Randomized Algorithms

• Guided random search technique
• Uses the payoff function to guide search

Genetic Algorithms (GAs)
GA
Efficiency
Specialized Algo.
P
Problems
Specialized algorithms best performance for
special problems Genetic algorithms good
performance over a wide range of problems
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GAFlowchart
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Encoding and Population - Example
Optimize f(x) x(8 x), x0,8
154
x 8/255 154 0 4.8313
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Fitness Evaluation - Example
Function f(x) x(8-x)
Chromosome Corresponding x Objective/
Fitness fn.
1 0 0 1 1 0 1 0
4.8313 15.3089
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Roulette Wheel Selection Example

Chromosome Fitness 1 15.3089 2 15.4091
3 4.8363 4 12.3975
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3
1
2

Spin
2
1
2
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Mating Pool
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Crossover Example
Here l (string length) 8. Let k (crossover
point) 5
Offspring formed
0 1 1 1 1

0 1 0
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Mutation- Example
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Pattern Classification
Classification
Supervised
Unsupervised
Presence of labelled data
All data unlabelled
Unsupervised
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Classification
Feature space
Decision Space
FL
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GAs for Pattern Classification

• Linear discriminant approach
• Modeling class boundaries using a number of
  hyperplanes
• Minimize the error.

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Modeling Class Boundaries Using A Number of
Hyperplanes
N-1 angles a , a , ..., a
Hyperplane in N dimensions
1
2
N-1
Perpendicular distance, d
H
H
H
1
1
1
1
a
a
a
a
d
d
a
N-1
N-1
N-1
N-1
1
1
2
Hyperplane H
Hyperplane 1
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Value of H
High overfitting the data
Low Poor/Incomplete approximation
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Evolve H automatically
Solution
Concept of variable string length
Chromosome 2
Fitness n - miss - H/ H
max
n size of training data miss number of
misclassified points H number of
hyperplanes H maximum number of
hyperplanes
max
Note miss has more dominance than H.
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Fitness Computation
1
2
2
2
2
1
1
2
2
2
1
1
misclassified
1
1
1
2
2
2
n 18 miss 4 H 4 H 8
fitness 18 - 4 - 4/8 13.5
max