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Proceedings Paper

Novel method of finding extreme edges in a convex set of N-dimension vectors
Author(s): Chia-Lun John Hu
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Paper Abstract

As we published in the last few years, for a binary neural network pattern recognition system to learn a given mapping {Um mapped to Vm, m=1 to M} where um is an N- dimension analog (pattern) vector, Vm is a P-bit binary (classification) vector, the if-and-only-if (IFF) condition that this network can learn this mapping is that each i-set in {Ymi, m=1 to M} (where Ymithere existsVmiUm and Vmi=+1 or -1, is the i-th bit of VR-m).)(i=1 to P and there are P sets included here.) Is POSITIVELY, LINEARLY, INDEPENDENT or PLI. We have shown that this PLI condition is MORE GENERAL than the convexity condition applied to a set of N-vectors. In the design of old learning machines, we know that if a set of N-dimension analog vectors form a convex set, and if the machine can learn the boundary vectors (or extreme edges) of this set, then it can definitely learn the inside vectors contained in this POLYHEDRON CONE. This paper reports a new method and new algorithm to find the boundary vectors of a convex set of ND analog vectors.

Paper Details

Date Published: 2 November 2001
PDF: 4 pages
Proc. SPIE 4476, Vision Geometry X, (2 November 2001); doi: 10.1117/12.447274
Show Author Affiliations
Chia-Lun John Hu, Southern Illinois Univ./Carbondale (United States)

Published in SPIE Proceedings Vol. 4476:
Vision Geometry X
Longin Jan Latecki; David M. Mount; Angela Y. Wu; Robert A. Melter, Editor(s)

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