Abstract
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 Pattern Recognition (PR), namely, one that involves Chaotic Neural Networks (CNNs). To achieve this, we enhance the basic model proposed by Adachi [1], referred to as Adachi’s Chaotic Neural Network (ACNN). Although the ACNN has been shown to be chaotic, we prove that it also has the property that the degree of “chaos” can be controlled; decreasing the multiplicity of the eigenvalues of the underlying control system, we can effectively decrease the degree of chaos, and conversely increase the periodicity. We then show that such a Modified ACNN (M-ACNN) 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 are presented. In this paper, which follows its companion paper [2], we analyze the M-ACNN for its stability and algorithmic issues. This paper also includes more comprehensive experimental results.
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References
Adachi M, Aihara K (1997) Associative Dynamics in a Chaotic Neural Network, Neural Networks 10:83–98
Calitoiu D, Oommen BJ, Nussbaum D (2005) Neural Network-based Chaotic Pattern Recognition — Part 1: Lyapunov Stability and Periodicity Issues, Submitted for PRIP’2005 (Eight International Conference on Pattern Recognition and Information Processing), Minsk, Belarus
Calitoiu D, Oommen BJ, Nussbaum D, Periodicity and Stability Issues of a Novel Chaotic Pattern Recognition Neural Network, Submitted for Publication, Unabridged version of the Paper
Theodoridis S, Koutroumbas K (1999) Pattern recognition. Academic Press
Bishop C M, Bishop C(2000) Neural Networks for Pattern Recognition. Oxford University Press
Ripley B (1996) Pattern Recognition and Neural Networks. Cambridge University Press
Fukunaga K (1990) Introduction to Statistical Pattern Recognition. Academic Press
Friedman M, Kandel A (1999) Introduction to Pattern Recognition, statistical, structural, neural and fuzzy logic approaches. World Scientific
Schurmann J (1996) Pattern classification, a unified view of statistical and neural approaches. John Wiley and Sons, New York
Kohonen T (1997) Self-Organizing Maps. Springer, Berlin
Fausett L (1994) Fundamentals of Neural Networks. Prentice Hall
Minorsky N (1962) Nonlinear Oscillations. D.Van Nostrand Company
Skarda CA, Freeman WJ (1987) How brains make chaos to make sense of the world, Behavioral and Brain Science 10:161–165
Freeman WJ (1992) Tutorial in neurobiology: From single neuron to brain chaos, International Journal of Bifurcation and Chaos 2:451–482
Shuai JW, Chen ZX, Liu RT, Wu BX (1997) Maximum hyperchaos in chaotic nonmonotonic neuronal networks, Physical Review E 56:890–893
Rosenstein MT, Collins JJ, De Luca CJ (1993) A practical method for calculating largest Lyapunov exponents from small data sets, Physica D 65:117–134
Geist K, Parlitz U, Lauterborn W (1990) Comparison of Different Methods for Computing Lyapunov Exponents, Progress of Theoretical Physics 83:875–893
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Calitoiu, D., Oommen, J.B., Nussbaum, D. (2005). Neural Network-Based Chaotic Pattern Recognition — Part 2: Stability and Algorithmic Issues. In: Kurzyński, M., Puchała, E., Woźniak, M., żołnierek, A. (eds) Computer Recognition Systems. Advances in Soft Computing, vol 30. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-32390-2_1
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DOI: https://doi.org/10.1007/3-540-32390-2_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-25054-8
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