Title :
Separating Points by Parallel Hyperplanes— Characterization Problem
Author :
Silvia Ghilezan;Jovanka Pantovic;Jovisa Zunic
Author_Institution :
Univ. of Novi Sad, Novi Sad
Abstract :
This paper deals with partitions of a discrete set S of points in a d-dimensional space, by h parallel hyperplanes. Such partitions are in a direct correspondence with multilinear threshold functions which appear in the theory of neural networks and multivalued logic. The characterization (encoding) problem is studied. We show that a unique characterization (encoding) of such multilinear partitions of S = {0,1,..., m - 1}d is possible within O(h ldr d2 ldr log to) bit rate per encoded partition. The proposed characterization (code) consists of(d+l)ldr(h+l) discrete moments having the order no bigger than 1. The obtained bit rate is evaluated depending on the mutual relations between h, d, and m. The optimality is reached in some cases.
Keywords :
"Encoding","Neural networks","Bit rate","Computer science","Object detection","Multivalued logic","Mathematics","Pattern classification","Boolean functions","Art"
Journal_Title :
IEEE Transactions on Neural Networks
DOI :
10.1109/TNN.2007.891678