Affiliations: [a] School of Computer Science and Engineering, University of Electronic Sci & Tech of China, Chengdu, China | [b] School of Computer Science, Carleton University, Ottawa, Canada
Note: [1] The second author was partially supported by NSERC, the Natural Sciences and Engineering Research Council of Canada. Some of the initial work of the first author was done while he was in Canada as a Visiting Scholar at Carleton University.
Abstract: Decision Theory and Pattern Recognition (PR) are inter-related. Indeed, if a practitioner is faced with a set of decisions and is required to make one based on the current “state of the world”, the problem is easily mapped into a PR problem where one maps the “state of the world” into the feature space, and the set of decisions onto the set of allowable classes. Of the various families of PR, Chaotic Pattern Recognition is a relatively new sub-field in which a system, which demonstrates chaotic behavior under normal conditions, resonates when it is presented with a pattern that it is trained with. The Adachi Neural Network (AdNN) is a classic neural structure which has been proven to demonstrate the phenomenon of Associative Memory (AM). In their pioneering paper Adachi and his co-authors showed that the AdNN also emanates periodic outputs on being exposed to trained patterns. This was later utilized by Calitoiu et al. to design systems which possibly possessed PR capabilities. In this paper, we show that the previously reported properties of the AdNN do not adequately describe the dynamics of the system. Rather, although it possesses far more powerful PR and AM properties than was earlier known, it goes through a spectrum of characteristics as one of its crucial parameters, α, changes. As α increases, the AdNN which is first an AM become quasi-chaotic (A formal explanation of this expression is given in the body of the paper.). The system is then distinguished by two phases which really do not have clear boundaries of demarcation. In the former of these phases it is quasi-chaotic for some patterns and periodic for others. In the latter of these, it exhibits properties that have been unknown – or rather, unreported – till now, namely, a PR capability which even recognizes masked or occluded patterns, in which the network resonates sympathetically for trained patterns while it is quasi-chaotic for untrained patterns. Finally, the system becomes completely periodic. The periodicity of the input patterns for trained and untrained inputs, and the understanding and demonstration of these properties, are to the best of our knowledge, novel.
Keywords: Chaotic Neural Networks (NNs), Chaotic Pattern Recognition, Adachi NN
