Accession Number:

ADA297408

Title:

The Mathematics of Measuring Capabilities of Artificial Neural Networks.

Descriptive Note:

Doctoral thesis,

Corporate Author:

AIR FORCE INST OF TECH WRIGHT-PATTERSON AFB OH

Personal Author(s):

Report Date:

1995-06-01

Pagination or Media Count:

121.0

Abstract:

Researchers rely on the mathematics of Vapnik and Chervonenkis to capture quantitatively the capabilities of specific artificial neural network ANN architectures. The quantifier is known as the V-C dimension, and is defined on functions or sets. Its value is the largest cardinality 1 of a set of vectors in Rd such that there is at least one set of vectors of cardinality 1 such that all dichotomies of that set into two sets can be implemented by the function or set. Stated another way, the V-C dimension of a set of functions is the largest cardinality of a set, such that there exists one set of that cardinality which can be shattered by the set of functions. A set of functions is said to shatter a set if each dichotomy of that set can be implemented by a function in the set. There is an abundance of research on determining the value of V-C dimensions of ANNs. In this document, research on V-C dimension is refined and extended yielding formulas for evaluating V-C dimension for the set of functions representable by a feed-forward, single hidden-layer perceptron artificial neural network.The fundamental thesis of this research is that the V-C dimension is not an appropriate quantifier of ANN capabilities. KAR P. 11

Subject Categories:

  • Numerical Mathematics
  • Computer Systems

Distribution Statement:

APPROVED FOR PUBLIC RELEASE