A General Approach to Construct RBF NetBased Classifier

1
A General Approach to Construct RBF Net-Based
Classifier

• Fabien Belloir
• Antoine Fache
• Alain Billat
• ESANN1999 Proceedings
• yfhuang_at_CSIE.NTU

2
Outline

• Introduction
• Algorithm presentation
• Benchmarking studies
• Conclusion
• References

3
Introduction

• General approach to construct RBF net-based
  classifier
• Neural Network Architectures
• Multi-Layer Perceptron
• Learning Vector Quantization
• RBF Network

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Multi-Layer Perceptron - MLP
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MLP (Cont)

• Combined with the backpropagation algorithm

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Learning Vector Quantization - LVQ
Proposed by Kohonen, 1990
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LVQ (Cont)

• A simple adaptive method of vector quantization
• Proposed by Kohonen, 1990
• Two layers
• Input layer
• Kohonen layer
• Fully connected between them

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Radial Basis Function Network - RBFN
Output Layer
Hidden Layer
Input Layer
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RBF Network (Cont)

• General equation of an output neurons
• Activation function - hypergaussian

10
Algorithm Presentation

• Principle
• Algorithm Description
• Basic Example
• Advantages

11
Principle

• Design Issue Iteratively subdivide each of the
  m basic classes Oj, disjoined but not necessarily
  convex, into a set of convex regions called
  clusters.
• Fully self-organized algorithm
• Without having to set up any parameters

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Algorithm Description

• Initialization gravity center
• Width definition
• Search for isolated point
• Learning
• The network weights wij are calculated by a least
  mean square method

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Basic Example

• Solving pattern recognition problem
• 3 classes, 2 attributes
• 100 points for each class

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Basic Example (Cont)
Figure. 1
Figure. 2
C1, C2, C3
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Basic Example (Cont)
Figure. 3
Figure. 4
9 iterations, 11 neurons
C1, C2, C3, C4
Why Center C2 move to Center C2 ? ? Minimal
Distance Assignment Principle
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Basic Example (Cont)
Figure. 5
The borders computed by the network for an output
sj0.5, j 1, 2, 3
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Major Advantages

• Only require training set (no step learning,
  threshold or other parameters)
• Robust and efficient classifier

18
Benchmarking Studies

• Dataset
• ELENA (Enhanced Learning for Evolutive Neural
  Architecture)
• Concentric
• Clouds
• Phoneme
• Iris
• Holdout method learn set test set
• Other competitive classifier
• KNN
• MLP
• LVQ

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Experimental Result
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Conclusion

• New simple incremental or self-organized RBF
  Network
• Without having to setup any parameters
• The robust and efficient classifier

21
References

• Comparing Generalization and Recognition
  Capability of Learning Vector Quantization and
  Multi-Layer Perceptron Architectures C. De
  Stefano, C. Sansone, M. Vento