Doctoral Dissertations

Date of Award

8-1997

Degree Type

Dissertation

Degree Name

Doctor of Philosophy

Major

Engineering Science

Major Professor

Belle. R. Upadhyaya

Committee Members

Raj P. Soni, R. E. Uhrig, Jack F. Wasserman

Abstract

In this work a novel artificial neural network (ANN) architecture has been developed and tested. This ANN is referred to as the PCA/HON network. This name refers to the combination of principal component analysis (PCA) and high order neuron (HON) which makes up the primary computational mechanism of the network.

This ANN has been developed by abstracting from neurophysiological findings certain basic concepts or principles of operation which may then be tested for suitability for Engineering, financial or other applications. The objective of this work has been to discover principles of neural computation rather than to perform detailed neurophysiological modeling.

The concept behind this ANN may be thought of as a local information maximization concept rather than a global error criterion.

This concept has four points.

  • Locality of Time

  • Locality of Network Topology

  • Preservation of Information

  • Feature Generation

Major components selected for this ANN include principal component analysis (PCA) and the high order neuron (HON). Another component, the decorrelated input associative memory (DIAM) is derived and a convergence proof is provided.

The DIAM algorithm is a biologically plausible associative memory algorithm based on Hebbian learning which is capable of storing a least squared error approximation of an unlimited number of patterns. The DIAM is a natural algorithm to follow PCA because PCA produces decorrelated outputs and DIAM requires uncorrelated inputs.

Two forms of the ANN have been developed: a batch mode network which uses conventional numerical methods and a recursive mode network which uses the weighted subspace learning algorithm (WSLA), a recursive PCA algorithm, and the recursive form of the DIAM algorithm. The recursive mode network has been run on the MasPar MP-2, a massively parallel single instruction multiple data (SIMD) computer.

The batch mode network performance is comparable to that of other functional approx- imation algorithms. The recursive mode network has produced preliminary results. Its primary accomplishment is to demonstrate the feasibility of the recursive algorithm.

The performance of the PCA/HON network has been demonstrated by performing next time step prediction for two chaotic attractors, the Rössler attractor and single channel human heart data. A signal validation application has been investigated. The results are comparable with other functional approximation methods.

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