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Computational intelligence: From mathematical point of view

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Chinese Science Bulletin

Abstract

A simple but illustrative survey is given on various approaches of computational intelligence with their features, applications and the mathematical tools involved, among which the simulated annealing, neural networks, genetic and evolutionary programming, self-organizing learning and adapting algorithms, hidden Markov models are recommended intensively. The common mathematical features of various computational intelligence algorithms are exploited. Finally, two common principles of concessive strategies implicated in many computational intelligence algorithms are discussed.

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References

  1. Li, G. J., Computational intelligence: An important field of research,Fundamental Study of Intelligent Computer ’94 (eds. Li, W., Huai, J. P., Bai, S.) (in Chinese), Beijing: Press of Tsinghua University, 1994, 9–12.

    Google Scholar 

  2. Dai, R. W., Semantics and grammar recognition based on artificial neural networks,Fundamental Study of Intelligent Computer’ 94 (Li, W., Huai, J. P., Bai, S.) (in Chinese), Beijing: Press of Tsinghua University, 1994, 1–5.

    Google Scholar 

  3. Sejnowski, T. J., Rosenberg, C. R., Parallel networks that learn pronounce English text,Complex Systems, 1987, (1): 145.

  4. Fogel, L. J., Owens, A. J., Walsh, M. J.,Artificial Intelligence Through Simulated Evolution, New York: John Wiley, 1966.

    Google Scholar 

  5. Holland, J. H., Genetic algorithm and the optimal allocations of trials,SIAM J. of Computing, 1973, 2(2): 88.

    Article  Google Scholar 

  6. Kirkpatrick, S., Gelatt, C. D., Jr., Vecchi, M. P., Optimization by simulated annealing,IBM Research Report, 1982, Re 9353.

  7. Macready, W. G., Siapas, A. G., Kauffman, S. A., Crilicality and parallelism in combinatorial optimization,Science, 1996, 271(5 Jan.): 56.

    Article  PubMed  CAS  Google Scholar 

  8. Khas’ minskii, R. Z., Application of random noise to optimization and recognition problems,Problems of Information Transmission, 1965, 1(3): 89.

    Google Scholar 

  9. van Laavhoven, P. J. M., Aarts, E. H. Y. L.,Simulation Annealing: Theory and Applications, Holland: D Reidel Publishing Company, 1987.

    Google Scholar 

  10. Holly, R., Stroock, D., Simulated annealing via Sobolev inequalities,Commun. Math. Phy., 1988, 115: 553.

    Article  Google Scholar 

  11. Chiang, T. S., Chow, Y., On the convergence rate of annealing Process,SAIM J. Control Optim., 1988, 26: 1455.

    Article  Google Scholar 

  12. Chiang, T. S., Chow, Y., A limit theory for a class of inhomogeneous Markov processes, Ann.of Probability, 1989, 17: 1483.

    Article  Google Scholar 

  13. Hwang, C. R., Sheu, S. J., Large-time behavior of perturbed diffusion Markov processes with application to the second eigenvalue problem for Fokker-Plank operators and simulated annealing,Acta Applicae Math., 1990, 19: 253.

    Article  Google Scholar 

  14. Chiang, T. S., Sheu, S. J., Diffusions for global optimization in Ad,SIAM J. Control Optm., 1987, 25: 737.

    Article  Google Scholar 

  15. Fang, H., Gong, G., Qian, M. P., Annealing of iterative stochastic schemes,SIAM J. Control Optim., 1997, 35(8): 1886.

    Article  Google Scholar 

  16. Szu, H. H., Hartley, H. L., Fast simulated annealing,Phy. lett. A, 1987, 123(3-4): 157.

    Article  Google Scholar 

  17. Szu, H. H., Hartley, H. L., Non-convex optimization by fast simulated annealing,Proc. of IEEE, 1987, 75(11): 1538.

    Article  Google Scholar 

  18. Fang, H., Gong, G., Qian, M. P., Disconvergence of Cauchy annealing,Science in China, Ser. A, 1996, 39(9): 945.

    Google Scholar 

  19. Li, Y., Qian, M. P., Convergence of TINA algorithms,Acta Sci. Natur. Univ. Pekin., 1996, 32(5): 557.

    Google Scholar 

  20. Lei, G., Qian, M. P., Generalized time invariant noise algorithm and related bifurcation problem,Tech. Report (in Chinese), Beijing: Peking University Press, 1997.

    Google Scholar 

  21. Fang, H., Gong, G., Qian, M. P., An improved annealing method and its large time behavior,Stochastic Processes and Their Appl., 1997, 71(1): 55.

    Article  Google Scholar 

  22. Kolmogorov, A. N., On the representation of continuous functions of many variables by superposition of continuous functions of one variable and addition,Dokl. Akad. Nauk. (in Russian), 1957, 144: 953.

    Google Scholar 

  23. Hopfield, J. J., Neural networks and physical systems with emergent collective computational ability, inProc. of Nat. Acad. Sci., USA, 1982, 79: 2554.

    Article  CAS  Google Scholar 

  24. Hopfield, J. J., Pattern recognition computation using action potential timing for stimulus representation,Nature, 1996, 6 (July).

  25. Zu, Z. B., Hu, G. Q., Kwong, C. P., Asymmetric Hopfield-type networks: theory and applications,Neural Networks, 1996, 9(3): 483.

    Article  Google Scholar 

  26. Hertz, J., Krogh, A., Palmer, G. R., Introduction to the theory of neural computation, LN Vol. 1, Santa Fe Institute,Studies in the Science of Complexity, Redwood City, California: Addison-Wesley Pub. Co., 1991.

    Google Scholar 

  27. Azencott, R., Boltzmann machines: high-order interactions and synchronous learning,Stochastic Models, Statistical Methods and Algorithms in Image Analysis. Lecture Notes in Statistics (ed. Barone, P.), Vol. 74, Berlin: Springer, 1992.

    Google Scholar 

  28. Zheng, J. L.,Artificial Neural Network (in Chinese), Beijing: Higher Education Publishing House, 1992.

    Google Scholar 

  29. Amit, D. J.,Modeling Brain Function, the World of Attractor Neural Networks, Cambridge: Cambridge University Press, 1989.

    Google Scholar 

  30. Geman, S., Bienenstock, E., Doursat, R., Neural networks and the bias/variance dilemma,Neural Computation, 1992, 4: 1

    Article  Google Scholar 

  31. Linsker, R., Self-organization in a perceptual network,Conputer, 1988, 21(3): 105.

    Google Scholar 

  32. Feng, J., Pan, H., Analysis of Linsker-Type Hebbian learning: rigorous results, 1993IEEE International Conference on Neural Networks, San Francisco, California, 1993.

  33. Albeverio, S., Feng, J., Qian, M. P., Role of noise in neural networks,Physics Rev. E, 1995, 52(6): 6593.

    Article  CAS  Google Scholar 

  34. Holland, J. H.,Adaptation in Natural and Artificial Systems, Ann Arbor, Chicargo: The Univ. of Michigan Press, 1975.

    Google Scholar 

  35. Kohonen, T.,Self-organization and Associative Memory, 3rd ed., Berlin: Springer-Verlag, 1989.

    Google Scholar 

  36. Burton, R. M., Pages, G., Self-organization and u.s. convergence of the one-dimensional Kohonen algorithm with nonuniformly distributed Stimuli,Stochastic Processes and Their Appl., 1993, 47(2): 249.

    Article  Google Scholar 

  37. Burton, R. M., Faris, W. G., A self-organizing cluster process,Ann. of Appl Prob., 1996, 6(4): 1232.

    Article  Google Scholar 

  38. Grossberg, S., Competitive learning: from interactive activation to adaptive resonance cognitive,Science, 1987, 1: 23.

    Google Scholar 

  39. Carpenter, G. A., Grossberg, S., The ART of adaptive pattern recognition by a selforganizing neural network,Trans. IEEE on Computer, 1988, 37(3): 77.

    Google Scholar 

  40. Qian, M. P., Competition learning approach of artificial neural networks,Fundamental Study of Intelligent Computer ’94 (eds. Li, W., Huai, J. P., Bai, S.) (in Chinese), Beijing: Press of Tsinghua University, 1994, 9–12.

    Google Scholar 

  41. Qian, M. P., Wu, D., The statistics and discussion on various distance of images and applications to fuzzifying technique, inProc. of the Asian Conference on Statistical Computing, Beijing, 1993, 181–184.

  42. Oja, E., Neural betworks, principle components, and subspace,International Journal of Neural Systems, 1989, 1: 61.

    Article  Google Scholar 

  43. Oja, E., Karrunen, J., On stochastic approximation of the eigenvectors and eigenvalues of the expectation of a random matrix,Journal of Mathematical Analysis and Applications, 1985, 100: 69.

    Article  Google Scholar 

  44. Benveniste, A., Metivier, M., Priouret, P.,Adaptive Algorithm and Stochastic Approximations, Berlin: Springer, 1990.

    Google Scholar 

  45. Chen, H. F., Zhu, Y. M.,Stochastic Approximations (in Chinese), Shanghai: Shanghai Science and Technology Press, 1996.

    Google Scholar 

  46. Kunsch, H., Geman, S., Kehagias, A., Hidden Markov random fields,Ann. Appl. Probab., 1993, 3(3): 577.

    Google Scholar 

  47. Rabiner, L. R., A tutorial on hidden Markov models and selected applications in speech recognition, inProc. IEEE, 1989, 77(2): 267.

    Article  Google Scholar 

  48. Rabiner, L. R., Juang Biing-hwang,Fundamentals of Speech Recognition, Hong Kong: Prince Hall International Inc., 1993.

    Google Scholar 

  49. Huo, Q., Chan Chorkin, Contextual vector quantization for speech recognition with discrete hidden Markov model,International Symposium on Speech Image Processing and Neural Networks, 13–16, April, 1994, Hong Kong, 698–701.

  50. Deng, M. H., Qian, M. P., Method of Recognition of handwriting Chinese characters and their realization based on hidden Markov fields,Symposium of the 3rd Session Intelligent Intersection of Computer in China and Intelligence Application Conference (eds. Wu, Q. Y., Qian, Y. L.), Beijing: Electronic Engineering Press, 1997, 204–208.

    Google Scholar 

  51. Churchill, G. A., Accurate restoration of DNA sequences,Case Study in Bayesian Statistics, Vol. II,Lecture Notes in Statistics (eds. Gatsonis, C., Hodges, J. S., Kass, R. E.et al.), 105, Berlin: Springer-Verlag, 1995, 90–148.

    Google Scholar 

  52. Leroux, B. G., Maximum-likelihood estimation for hidden Markov modeling,Stoc. Processes and their Appl., 1992, 40(1): 127.

    Article  Google Scholar 

  53. Elliott, R. J., Aggoun, L., Moore, J. B.,Hidden Markov Models, Berlin: Springer-Verlag, 1995.

    Google Scholar 

  54. Ho Yu-chi Larry, Soft Optimization of Hard Problem, inProc. of International Conference on Control and Information (invited talk), Hong Kong, 1996.

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Qian, M., Gong, G. Computational intelligence: From mathematical point of view. Chin. Sci. Bull. 44, 865–880 (1999). https://doi.org/10.1007/BF02885056

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