Domains of attraction in autoassociative memory networks for character pattern recognition

Abstract

An autoassociative memory network is constructed by storing character pattern vectors whose components consist of a small positive number ε and 1−ε. Although its connection weights and threshold values can not be determined only by this storing condition, it is proved that the output function of the network is contractive in a region around each stored pattern, if ε 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 contraction mapping analysis. In addition to this region, larger domains of attraction 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. Moreover, an autoassociative memory model having large domains of attraction is proposed. This model has symmetric connection weights and is successfully applied to character pattern recognition.