A multivalued bidirectional associative memory operating on a complex domain

Lee Donq-Liang; Wang Wen-June

doi:10.1016/S0893-6080(98)00078-1

A multivalued bidirectional associative memory operating on a complex domain

Lee Donq-Liang, Wang Wen-June

Department of Electrical Engineering

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

43 Scopus citations

Abstract

A bidirectional associative memory (BAM) with complex states and connection weights is investigated in this paper. The states are represented by quantization values defined on the unit circle of the complex plane. A given Lyapunov function indicates that the proposed complex domain BAM (CDBAM) is bidirectionally stable no matter which operation (synchronous or asynchronous) is used. We also prove that all the equilibrium (fixed) points of CDBAM correspond to local energy minima so that the design problem can be solved by a gradient descent algorithm. Finally, a gradient descent algorithm in the complex domain is derived to design the weight matrix of CDBAM. Several computer simulations are performed to illustrate the validity, capacity, attractivity and the applications of the CDBAM.

Original language	English
Pages (from-to)	1623-1635
Number of pages	13
Journal	Neural Networks
Volume	11
Issue number	9
DOIs	https://doi.org/10.1016/S0893-6080(98)00078-1
State	Published - Dec 1998

Keywords

Bidirectional associative memory
Bidirectional stability
Complex domain
Gradient descend algorithm
Lyapunov function
Multivalued associative memory

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10.1016/S0893-6080(98)00078-1

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title = "A multivalued bidirectional associative memory operating on a complex domain",

abstract = "A bidirectional associative memory (BAM) with complex states and connection weights is investigated in this paper. The states are represented by quantization values defined on the unit circle of the complex plane. A given Lyapunov function indicates that the proposed complex domain BAM (CDBAM) is bidirectionally stable no matter which operation (synchronous or asynchronous) is used. We also prove that all the equilibrium (fixed) points of CDBAM correspond to local energy minima so that the design problem can be solved by a gradient descent algorithm. Finally, a gradient descent algorithm in the complex domain is derived to design the weight matrix of CDBAM. Several computer simulations are performed to illustrate the validity, capacity, attractivity and the applications of the CDBAM.",

keywords = "Bidirectional associative memory, Bidirectional stability, Complex domain, Gradient descend algorithm, Lyapunov function, Multivalued associative memory",

author = "Lee Donq-Liang and Wang Wen-June",

note = "Funding Information: This work was supported by the National Science Council, Taiwan, People's Republic of China under the Grant NSC87-2213-E233-002. The authors would like to thank the anonymous reviewers for comments which have greatly improved the presentation of this paper. ",

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AU - Wen-June, Wang

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N2 - A bidirectional associative memory (BAM) with complex states and connection weights is investigated in this paper. The states are represented by quantization values defined on the unit circle of the complex plane. A given Lyapunov function indicates that the proposed complex domain BAM (CDBAM) is bidirectionally stable no matter which operation (synchronous or asynchronous) is used. We also prove that all the equilibrium (fixed) points of CDBAM correspond to local energy minima so that the design problem can be solved by a gradient descent algorithm. Finally, a gradient descent algorithm in the complex domain is derived to design the weight matrix of CDBAM. Several computer simulations are performed to illustrate the validity, capacity, attractivity and the applications of the CDBAM.

AB - A bidirectional associative memory (BAM) with complex states and connection weights is investigated in this paper. The states are represented by quantization values defined on the unit circle of the complex plane. A given Lyapunov function indicates that the proposed complex domain BAM (CDBAM) is bidirectionally stable no matter which operation (synchronous or asynchronous) is used. We also prove that all the equilibrium (fixed) points of CDBAM correspond to local energy minima so that the design problem can be solved by a gradient descent algorithm. Finally, a gradient descent algorithm in the complex domain is derived to design the weight matrix of CDBAM. Several computer simulations are performed to illustrate the validity, capacity, attractivity and the applications of the CDBAM.

KW - Bidirectional associative memory

KW - Bidirectional stability

KW - Complex domain

KW - Gradient descend algorithm

KW - Lyapunov function

KW - Multivalued associative memory

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JO - Neural Networks

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A multivalued bidirectional associative memory operating on a complex domain

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Keywords

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