Intelligent Numerical Computation1 Center:Width:.

Intelligent Numerical Computation 1

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Radial basis function network


Find an interpolation function with N RBFs


Or

Solve


A class of RBFs


Generalization to multi-dimensional target

Interpolation conditions

Interpolation function


M<<N

Adapted by an algorithm

Adapted by an algorithm

A bias


A RBF network

Or in matrix


Universal approximation


Extended basis functions


where


Minimize the cost function


I


Advanced clustering algorithms

II LVQIII K-means algorithmIV Kohonen self-organizing algorithm


to

where


Assignment #3

Implement a training algorithm for a RBF network•Multi-dimensional input space•One-dimensional output space•You can select supervised training or two-stage training or more advanced training algorithm•Your program should be able to read a training file and a testing file to evaluate performance. The last column of the training file will be the desired output.


Variants


Model size vs generalization

Minimal model size and maximal generalization


Applications

http://lib.stat.cmu.edu/datasets/

http://www.cs.toronto.edu/~delve/data/datasets.html

http://www.phys.uni.torun.pl/neural/node12.html

Radial basis function interpolation for 3-D ultrasound

http://svr-www.eng.cam.ac.uk/~ahg/rnr20/publications.html

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