On Characterization of Attractor Basins of Fuzzy Multiple Attractor Cellular Automata

• Autorzy: Maji P.
• Języki publikacji: EN

Abstrakty

EN

Two new operators, namely, dependency vector (DV) and derived complement vector (DCV) are introduced in this paper to characterize the attractor basins of the additive fuzzy cellular automata (FCA) based associative memory, termed as fuzzy multiple attractor cellular automata (FMACA). The introduction of DV and DCV makes the complexity of the attractor basin identification algorithm linear in time. The characterization of the FMACA using DV and DCV establishes the fact that the FMACA provides both equal and unequal size of attractor basins. Finally, a set of algorithms is proposed to synthesize the FCA rules, attractors, and predecessors of attractors from the given DV and DCV in linear time complexity.

Słowa kluczowe

EN

cellular automata; fuzzy cellular automata; associative memory; attractor basin

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2008
• Tom: Vol. 86, nr 1-2
• Strony: 143--168
• Opis fizyczny: bibliogr. 32 poz., tab.

Twórcy

autor

Maji P.

• Machine Intelligence Unit, Indian Statistical Institute, 203 B. T. Road, Kolkata, 700 108, India,

Bibliografia

• [1] Adamatzky, A. I.: Hierarchy of Fuzzy Cellular Automata, Fuzzy Sets and Systems, 62(2), 1994, 167-174.
• [2] Adamatzky, A. I.: Identification of Cellular Automata, Taylor and Francis Inc., Bristol, 1994.
• [3] Buhmann, J., Divko, R., Schulter, K.: Associative Memory with High Information Content, Physical Review A, 39, 1989, 2689-2692.
• [4] Carpenter, G. A.: NeuralNetworkModel for Pattern Recognition and AssociativeMemory, Neural Networks, 2(4), 1989, 243-257.
• [5] Cattaneo, G., Flocchini, P., Mauri, G., Vogliotti, C. Q., Santoro, N.: Cellular Automata in Fuzzy Backgrounds, Physica D, 105, 1997, 105-120.
• [6] Chady, M., Poli, R.: Evolution of Cellular Automaton Based Associative Memories, Second On-Line World Conference on Soft Computing in Engineering Design and Manufacturing, 1997, 1-8.
• [7] Chattopadhyay, S., Adhikari, S., Sengupta, S., Pal, M.: Highly Regular, Modular, and Cascadable Design of Cellular Automata Based Pattern Classifier, IEEE Transactions on VLSI Systems, 8(6), December 2000, 724-735.
• [8] Chua, L. O., Yang, L.: Cellular Neural Networks: Application, IEEE Transactions on Circuits and Systems, 35(10), 1988, 1273-1290.
• [9] Chua, L. O., Yang, L.: Cellular Neural Networks: Theory, IEEE Transactions on Circuits and Systems, 35(10), 1988, 1257-1272.
• [10] Dougherty, J., Kohavi, R., Sahami, M.: Supervised and Unsupervised Discretization of Continuous Features, Proceedings of the 12th International Conference on Machine Learning, San Francisco, CA: Morgan Kaufmann, 1995, 194-202.
• [11] Flocchini, P., Geurts, F., Mingarelli, A., Santoro, N.: Convergence and Aperiodicity in Fuzzy Cellular Automata: Revisiting Rule 90, Physica D, 142, 2000, 20-28.
• [12] Flocchini, P., Geurts, F., Santoro, N.: CA-Like Error Propagation in Fuzzy CA, Parallel Computing, 23(11), 1997, 1673-1682.
• [13] Ganguly, N., Maji, P., Dhar, S., Sikdar, B. K., Chaudhuri, P. P.: Evolving Cellular Automata as Pattern Classifier, Proceedings of the Fifth International Conference on Cellular Automata for Research and Industry, ACRI 2002, Switzerland, Lecture Notes in Computer Science, Springer, 2493, October 2002, 56-68.
• [14] Ganguly, N., Maji, P., Sikdar, B. K., Chaudhuri, P. P.: Design and Characterization of Cellular Automata Based Associative Memory for Pattern Recognition, IEEE Transactions on System, Man and Cybernetics, Part B, 34(1), February 2004, 672-678.
• [15] Hertz, J., Krogh, A., Palmer, R. G.: Introduction to the Theory of Neural Computation, Santa Fe Institute Studies in the Sciences of Complexity, Addison Wesley, 1991.
• [16] Hopfield, J. J.: Neural Networks and Physical System With Emergent Collective Computational Abilities, Proceedings of National Academic of Sciences, 79, 1982, 2554-2558.
• [17] Hopfield, J. J.: Pattern Recognition Computation Using Action Potential Timings for Stimulus Representations, Nature, 376, 1995, 33-36.
• [18] Jen, E.: Invariant Strings and Pattern Recognizing Properties of 1D CA, Journal of Statistical Physics, 43, 1986.
• [19] Kohavi, R., Sahami,M.: Error Based and Entropy Based Discretization of Continuous Features, Proceedings of the 2nd International Conference on Knowledge Discovery and Data Mining, Portland, OR: AAAI Press, 1996, 114-119.
• [20] Li, W., Packard, N. H., Langton, C. G.: Transition Phenomena in Cellular Automata Rule Space, Physica D, 45, 1990.
• [21] Lipschurtz, S.: Linear Algebra, Schaum's Outline Series, McGraw-Hill International Editions, 1991.
• [22] Maji, P., Chaudhuri, P. P.: FMACA: A Fuzzy Cellular Automata Based Pattern Classifier, Proceedings of the 9th International Conference on Database Systems for Advanced Applications, South Korea, Lecture Notes in Computer Science, Springer, 2973, March 2004, 494-505.
• [23] Maji, P., Chaudhuri, P. P.: Fuzzy Cellular Automata for Modeling Pattern Classifier, IEICE Transactions on Information and Systems, E88-D(4), April 2005, 691-702.
• [24] Maji, P., Chaudhuri, P. P.: RBFFCA: A Hybrid Pattern Classifier Using Radial Basis Function and Fuzzy Cellular Automata, Fundamenta Informaticae, 78(3), August 2007, 369-396.
• [25] Maji, P., Ganguly, N., Chaudhuri, P. P.: Error Correcting Capability of Cellular Automata Based Associative Memory, IEEE Transactions on System, Man and Cybernetics, Part A, 33(4), July 2003, 466-480.
• [26] Maji, P., Nandi, R., Chaudhuri, P. P.: Application of Fuzzy Cellular Automata (FCA) for Modeling Tree-Structured Pattern Classifier, Proceedings of the 1st Indian International Conference on Artificial Intelligence, IICAI 2003, Hyderabad, India, December 2003, 1220-1233.
• [27] Maji, P., Nandi, R., Chaudhuri, P. P.: Design of Fuzzy Cellular Automata (FCA) Based Pattern Classifier, Proceedings of the Fifth International Conference on Advances in Pattern Recognition, ICAPR 2003, Calcutta, India, December 2003, 113-117.
• [28] Maji, P., Shaw, C., Ganguly, N., Sikdar, B. K., Chaudhuri, P. P.: Theory and Application of Cellular Automata for Pattern Classification, Fundamenta Informaticae, 58(3-4), December 2003, 321-354.
• [29] Maji, P., Sikdar, B. K., Chaudhuri, P. P.: Cellular Automata Evolution for Pattern Classification, Proceedings of the 6th International Conference on Cellular Automata for Research and Industry, ACRI 2004, Amsterdam, The Netherlands, Lecture Notes in Computer Science, Springer, 3305, October 2004, 660-669.
• [30] Morita, K., Ueno, S.: Parallel Generation and Parsing of Array Languages Using Reversible Cellular Automata, International Journal of Pattern Recognition and Artificial Intelligence, 8, 1994, 543-561.
• [31] Raghavan, R.: Cellular Automata in Pattern Recognition, Information Sciences, 70(1-2), 1993, 145-177.
• [32] Wolfram, S.: Cellular Automata and Complexity, chapter 4, Westview Press, 2002, 159-202