Abstract
An overview is given of certain underlying relationships between neural networks and Iterated Function Systems. Possible applications to data compression and stochastic learning automata are discussed.
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References
Barnsley, M.F., Demko, S., Elton, J., and Geronimo, J., Markov processes arising from iteration with place-dependent probabilities, Pre-print, Georgia Inst. Technology, 1985.
Barnsley, M.F., Fractals Everywhere, San Diego: Academic Press, 1988.
Barnsley, M.F., and Sloan, A.D., A better way to compress images, Byte, Vol. 13, pp. 215–223, 1988.
Barto, A.G., Sutton, R.S., and Brouwer, P.S., Associative search network, Biol. Cybern., Vol. 40, pp. 201–211, 1981.
Barto, A.G., and Anandan, P., Pattern-recognising stochastic learning automata, IEEE Trans. Syst. Man and Cybrn., Vol. 15, pp. 360–375, 1985.
Bressloff, P.C., Neural networks and random iterative maps, in Neural Computation, Mannion, C, and Taylor, J.G., Eds., pp. 155–162, Bristol, UK: Adam Hilger, 1989.
Bressloff, P.C., and Stark, J., Associative reinforcement learning based on iterated function systems, submitted to IEEE Trans. Syst. Man and Cybern., 1989.
Bressloff, P.C., and Taylor, J.G., Random iterative networks, Phys. Rev. A, Vol. 41, pp. 1126–1137, 1990.
Elton, J.H., An ergodic theorem for iterated maps, Ergod. Th. and Dynam. Sys., Vol. 7, pp. 481–488, 1987.
Erdos, P., On a family of symmetric Bernouilli convolutions, Amer. Jour. Math., Vol. 61, pp. 974–976, 1939.
Federer, H., Geometric Measure Theory, New York: Springer-Verlag, 1969.
Falconer, K.J., The Geometry of Fractal Sets, Cambridge, UK: Cambridge Univ. Press, 1985.
Hutchinson, J.F., Fractals and self-similarity,Indiana Univ. Jour, of Math., Vol. 30, pp. 713–747, 1981.
Karlin, S., Some random walks arising in learning models, Pacific Jour. Math., Vol. 3, pp. 725–756, 1953.
Lakshmivarahan, S., Learning Algorithms Theory and Applications, New York: Springer-Verlag, 1981.
Narendra, K.S., and Thathachar, M.A.L., Learning automata—A survey, IEEE, Trans. Syst. Man and Cybern., Vol. 4, pp. 323–334, 1974.
Norman, M.F., Some convergence theorems for stochastic learning models with distance diminishing operators, Jour. Math. Psychol, Vol. 5, pp. 61–101, 1968.
Norman, M.F., Markov Processes and Learning Models, New York: Academic Press, 1972.
Prusinkiewicz, P., and Sandness, G., Koch curves as attractors and repellors, IEEE Comput. Graph, and Appl, Vol. 8, pp. 26–40, 1988.
Reddaway, S.F., Fractal graphics and image compression on a DAP, in International Specialist Seminar on the Design and Application of Parallel Digital Processors(IEE Conf. Publ. 298), p. 201, 1988.
Seneta, W., Non-negative Matrices and Markov Chains, New York: Springer-Verlag, 1981.
Stark, J., Iterated function systems as neural networks, submitted to Neural Networks, 1989.
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Bressloff, P.C., Stark, J. (1991). Neural Networks, Learning Automata and Iterated Function Systems. In: Crilly, A.J., Earnshow, R.A., Jones, H. (eds) Fractals and Chaos. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3034-2_8
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DOI: https://doi.org/10.1007/978-1-4612-3034-2_8
Publisher Name: Springer, New York, NY
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