Novel method of finding extreme edges in a convex set of N-dimension vectors

Chia-Lun John Hu

doi:10.1117/12.447274

2 November 2001 Novel method of finding extreme edges in a convex set of N-dimension vectors

Chia-Lun John Hu

Proceedings Volume 4476, Vision Geometry X; (2001) https://doi.org/10.1117/12.447274
Event: International Symposium on Optical Science and Technology, 2001, San Diego, CA, United States

Abstract

As we published in the last few years, for a binary neural network pattern recognition system to learn a given mapping {U_m mapped to V_m, m=1 to M} where u_m is an N- dimension analog (pattern) vector, V_m 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 {Y_mi, m=1 to M} (where Y_mithere existsV_miU_m and V_mi=+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.

Citation Download Citation

Chia-Lun John Hu "Novel method of finding extreme edges in a convex set of N-dimension vectors", Proc. SPIE 4476, Vision Geometry X, (2 November 2001); https://doi.org/10.1117/12.447274

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