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Proceedings Paper

Convexity of learning vectors and their N-dimension boundary
Author(s): Chia-Lun John Hu
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Paper Abstract

Most neural networks consisting of discrete (or sign- function) neurons can be studied by discrete mathematics and N-dimension geometry. Particularly, the supervised learning of a feed-forward neural system is crucially related to the geometry of N-dimension convex cones in the N-space. It is shown in this paper that to learn a set of pattern sample vectors forming a convex cone in the N-space, it is only necessary to learn the boundary vectors (or the extreme edges) of this cone, which then makes the learning much more efficient. This paper provides a novel approach to test the convexity of a set of N-vectors (given numerically in an Euclidean N-space) and to find the boundary vectors of this set if it is convex.

Paper Details

Date Published: 5 April 2002
PDF: 5 pages
Proc. SPIE 4668, Applications of Artificial Neural Networks in Image Processing VII, (5 April 2002); doi: 10.1117/12.461678
Show Author Affiliations
Chia-Lun John Hu, Southern Illinois Univ./Carbondale (United States)

Published in SPIE Proceedings Vol. 4668:
Applications of Artificial Neural Networks in Image Processing VII
Nasser M. Nasrabadi; Aggelos K. Katsaggelos, Editor(s)

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