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https://open.uns.ac.rs/handle/123456789/16095
Title: | Separating points by parallel hyperplanes-characterization problem | Authors: | Gilezan, Silvia Pantović, Jovanka Žunić J. |
Issue Date: | 1-Sep-2007 | Journal: | IEEE Transactions on Neural Networks | 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 · d2 · log m) bit rate per encoded partition. The proposed characterization (code) consists of (d+1) · (h+1) 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. © 2007 IEEE. | URI: | https://open.uns.ac.rs/handle/123456789/16095 | ISSN: | 10459227 | DOI: | 10.1109/TNN.2007.891678 |
Appears in Collections: | FTN Publikacije/Publications |
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