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Domains of attraction in autoassociative memory networks

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Abstract

An autoassociative memory network is constructed by storing reference pattern vectors whose components consist of a small positive number ∈ and 1-∈. Although its connection weights can not be determined only by this storing condition, it is proved that the output function of the network becomes a contraction mapping in a region around each stored pattern if ∈ is sufficiently small. This implies that the region is a domain of attraction in the network. The shape of the region is clarified in our analysis. Domains of attraction larger than this region are also found. Any noisy pattern vector in such domains, which may have real valued components, can be recognized as one of the stored patterns. We propose a method for determining connection weights of the network, which uses the shape of the domains of attraction. The model obtained by this method has symmetric connection weights and is successfully applied to character pattern recognition.

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Authors and Affiliations

  1. Department of Control Engineering and Science, Kyushu Institute of Technology, 820, Iizuka, Japan

    Koichi Niijima

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  1. Koichi Niijima
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Koichi Niijima, Ph. D: He is a Professor of Department of Control Engineering and Science, Kyushu Institute of Technology. He received the B. S. degree in 1967, the M. S. degree in 1969 and the Dr. Sci. degree in 1977 from Kyushu University. He has been working on learning algorithms of neural networks, pattern recognition by neural networks and wavelet analysis of image.

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Niijima, K. Domains of attraction in autoassociative memory networks. New Gener Comput 12, 395–407 (1994). https://doi.org/10.1007/BF03037354

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  • DOI: https://doi.org/10.1007/BF03037354

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