A Geometric Approach to Properties of the Discrete-Time Cellular Neural Network

Holger Magnussen; Josef A. Nossek

doi:10.1109/81.329723

A Geometric Approach to Properties of the Discrete-Time Cellular Neural Network

Holger Magnussen, Josef A. Nossek

Chair of Circuit Theory and Signal Processing (2008 — 2021)

Technical University of Munich

Research output: Contribution to journal › Article › peer-review

2 Scopus citations

Abstract

Using the available theory on Linear Threshold Logic, the Discrete-Time Cellular Neural Network (DTCNN) is studied from a geometrical point of view. Different modes of operation are specified. A bound on the number of possible mappings is given for the case of binary inputs. The mapping process in a cell of the network is interpreted in the input space and the parameter space. Worst-case and average-case accuracy conditions are given, and a sufficient worst-case bound on the number of bits required to store the network parameters for the case of binary input signals is derived. Methods for optimizing the robustness of DTCNN parameters for certain regions of the parameter space are discussed.

Original language	English
Pages (from-to)	625-634
Number of pages	10
Journal	IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications
Volume	41
Issue number	10
DOIs	https://doi.org/10.1109/81.329723
State	Published - Oct 1994

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title = "A Geometric Approach to Properties of the Discrete-Time Cellular Neural Network",

abstract = "Using the available theory on Linear Threshold Logic, the Discrete-Time Cellular Neural Network (DTCNN) is studied from a geometrical point of view. Different modes of operation are specified. A bound on the number of possible mappings is given for the case of binary inputs. The mapping process in a cell of the network is interpreted in the input space and the parameter space. Worst-case and average-case accuracy conditions are given, and a sufficient worst-case bound on the number of bits required to store the network parameters for the case of binary input signals is derived. Methods for optimizing the robustness of DTCNN parameters for certain regions of the parameter space are discussed.",

author = "Holger Magnussen and Nossek, {Josef A.}",

note = "Funding Information: Manuscript received December 20, 1993. Holger Magnussen is supported by a grant from the Emst-von-Siemens Foundation. This paper was recommended by Associate Editor Mona E. Zaghloul. The authors are with the Institute for Network Theory and Circuit Design, Technical University Munich, Munich, Germany. IEEE Log Number 9405335.",

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A Geometric Approach to Properties of the Discrete-Time Cellular Neural Network

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