Periodicity and stability issues of a chaotic pattern recognition neural network

Traditional pattern recognition (PR) systems work with the model that the object to be recognized is characterized by a set of features, which are treated as the inputs. In this paper, we propose a new model for PR, namely one that involves chaotic neural networks (CNNs). To achieve this, we enhance the basic model proposed by Adachi (Neural Netw 10:83–98, 1997), referred to as Adachi’s Neural Network (AdNN), which though dynamic, is not chaotic. We demonstrate that by decreasing the multiplicity of the eigenvalues of the AdNN’s control system, we can effectively drive the system into chaos. We prove this result here by eigenvalue computations and the evaluation of the Lyapunov exponent. With this premise, we then show that such a Modified AdNN (M-AdNN) has the desirable property that it recognizes various input patterns. The way that this PR is achieved is by the system essentially sympathetically “resonating” with a finite periodicity whenever these samples (or their reasonable resemblances) are presented. In this paper, we analyze the M-AdNN for its periodicity, stability and the length of the transient phase of the retrieval process. The M-AdNN has been tested for Adachi’s dataset and for a real-life PR problem involving numerals. We believe that this research also opens a host of new research avenues. Research partially supported by the Natural Sciences and Engineering Research Council of Canada.

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Dragos Calitoiu (Corresponding author)Email:

B. John OommenEmail:

Doron NussbaumEmail:

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Dragos Calitoiu   was born in Iasi, Romania on May 7, 1968. He obtained his Electronics degree in 1993 from the Polytechnical University of Bucharest, Romania, and the Ph. D. degree in 2006, from Carleton University, in Ottawa, Canada. He is currently a Postdoctoral Fellow with the Health Policy Research Division of Health Canada. His research interests include Pattern Recognition, Machine Learning, Learning Automata, Chaos Theory and Computational Neuroscience. B. John Oommen   was born in Coonoor, India on September 9, 1953. He obtained his B. Tech. degree from the Indian Institute of Technology, Madras, India in 1975. He obtained his M. E. from the Indian Institute of Science in Bangalore, India in 1977. He then went on for his M. S. and Ph. D. which he obtained from Purdue University, in West Lafayettte, Indiana in 1979 and 1982, respectively. He joined the School of Computer Science at Carleton University in Ottawa, Canada, in the 1981–1982 academic year. He is still at Carleton and holds the rank of a Full Professor. His research interests include Automata Learning, Adaptive Data Structures, Statistical and Syntactic Pattern Recognition, Stochastic Algorithms and Partitioning Algorithms. He is the author of more than 260 refereed journal and conference publications and is a Fellow of the IEEE and a Fellow of the IAPR. Dr. Oommen is on the Editorial Board of the IEEE Transactions on Systems, Man and Cybernetics, and Pattern Recognition. Doron Nussbaum   received his B.Sc. degree in mathematics and computer science from the University of Tel-Aviv, Israel in 1985, and the M. C. S. and Ph. D. degrees in computer science from Carleton University, Ottawa, Canada in 1988 and 2001, respectively. From 1988 to 1991 he worked for Tydac Technologies as a Manager of Research and Development. His work at Tydac focused on the development of a geographical information system. From 1991 to 1994, he worked for Theratronics as senior software consultant where he worked on the company’s cancer treatment planning software (Theraplan). From 1998 to 2001 he worked for SHL Systemshouse as a senior technical architect. In 2001 he joined the School of Computer Science at Carleton University as an Associate Professor. Dr. Nussbaum’s main research interests are medical computing, computational geometry, robotics and algorithms design.