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Proceedings Paper

Evaluating the Vapnik-Chervonenkis dimension of artificial neural networks using the Poincare' polynomial
Author(s): Mark E. Oxley; Martha Alvey Carter
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Paper Abstract

The Vapnik-Chervonenkis (V-C) dimension of a set of functions representing a feed-forward, multi-layered, single output artificial neural network (ANN) with hard-limited activation functions can be evaluated using the Poincare polynomial of the implied hyperplane arrangement. This ANN geometrically is a hyperplane arrangement configured to dichotomize a signed set (i.e., a two-class set). Since it is known that the cut- intersections of the hyperplane arrangement forms a semi- lattice, then the Poincare polynomial can be used to evaluate certain geometric invariants of this semi-lattice, in particular, the cardinality of the resultant chamber set of the arrangements, which is shown to be the V-C dimension. From this theory comes a stable formula to compute the V-C dimension values.

Paper Details

Date Published: 22 March 1999
PDF: 8 pages
Proc. SPIE 3722, Applications and Science of Computational Intelligence II, (22 March 1999); doi: 10.1117/12.342902
Show Author Affiliations
Mark E. Oxley, Air Force Institute of Technology (United States)
Martha Alvey Carter, National Air Intelligence Ctr. (United States)

Published in SPIE Proceedings Vol. 3722:
Applications and Science of Computational Intelligence II
Kevin L. Priddy; Paul E. Keller; David B. Fogel; James C. Bezdek, Editor(s)

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