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.
Similar content being viewed by others
References
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.
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.
Sejnowski, T. J., Rosenberg, C. R., Parallel networks that learn pronounce English text,Complex Systems, 1987, (1): 145.
Fogel, L. J., Owens, A. J., Walsh, M. J.,Artificial Intelligence Through Simulated Evolution, New York: John Wiley, 1966.
Holland, J. H., Genetic algorithm and the optimal allocations of trials,SIAM J. of Computing, 1973, 2(2): 88.
Kirkpatrick, S., Gelatt, C. D., Jr., Vecchi, M. P., Optimization by simulated annealing,IBM Research Report, 1982, Re 9353.
Macready, W. G., Siapas, A. G., Kauffman, S. A., Crilicality and parallelism in combinatorial optimization,Science, 1996, 271(5 Jan.): 56.
Khas’ minskii, R. Z., Application of random noise to optimization and recognition problems,Problems of Information Transmission, 1965, 1(3): 89.
van Laavhoven, P. J. M., Aarts, E. H. Y. L.,Simulation Annealing: Theory and Applications, Holland: D Reidel Publishing Company, 1987.
Holly, R., Stroock, D., Simulated annealing via Sobolev inequalities,Commun. Math. Phy., 1988, 115: 553.
Chiang, T. S., Chow, Y., On the convergence rate of annealing Process,SAIM J. Control Optim., 1988, 26: 1455.
Chiang, T. S., Chow, Y., A limit theory for a class of inhomogeneous Markov processes, Ann.of Probability, 1989, 17: 1483.
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.
Chiang, T. S., Sheu, S. J., Diffusions for global optimization in Ad,SIAM J. Control Optm., 1987, 25: 737.
Fang, H., Gong, G., Qian, M. P., Annealing of iterative stochastic schemes,SIAM J. Control Optim., 1997, 35(8): 1886.
Szu, H. H., Hartley, H. L., Fast simulated annealing,Phy. lett. A, 1987, 123(3-4): 157.
Szu, H. H., Hartley, H. L., Non-convex optimization by fast simulated annealing,Proc. of IEEE, 1987, 75(11): 1538.
Fang, H., Gong, G., Qian, M. P., Disconvergence of Cauchy annealing,Science in China, Ser. A, 1996, 39(9): 945.
Li, Y., Qian, M. P., Convergence of TINA algorithms,Acta Sci. Natur. Univ. Pekin., 1996, 32(5): 557.
Lei, G., Qian, M. P., Generalized time invariant noise algorithm and related bifurcation problem,Tech. Report (in Chinese), Beijing: Peking University Press, 1997.
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.
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.
Hopfield, J. J., Neural networks and physical systems with emergent collective computational ability, inProc. of Nat. Acad. Sci., USA, 1982, 79: 2554.
Hopfield, J. J., Pattern recognition computation using action potential timing for stimulus representation,Nature, 1996, 6 (July).
Zu, Z. B., Hu, G. Q., Kwong, C. P., Asymmetric Hopfield-type networks: theory and applications,Neural Networks, 1996, 9(3): 483.
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.
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.
Zheng, J. L.,Artificial Neural Network (in Chinese), Beijing: Higher Education Publishing House, 1992.
Amit, D. J.,Modeling Brain Function, the World of Attractor Neural Networks, Cambridge: Cambridge University Press, 1989.
Geman, S., Bienenstock, E., Doursat, R., Neural networks and the bias/variance dilemma,Neural Computation, 1992, 4: 1
Linsker, R., Self-organization in a perceptual network,Conputer, 1988, 21(3): 105.
Feng, J., Pan, H., Analysis of Linsker-Type Hebbian learning: rigorous results, 1993IEEE International Conference on Neural Networks, San Francisco, California, 1993.
Albeverio, S., Feng, J., Qian, M. P., Role of noise in neural networks,Physics Rev. E, 1995, 52(6): 6593.
Holland, J. H.,Adaptation in Natural and Artificial Systems, Ann Arbor, Chicargo: The Univ. of Michigan Press, 1975.
Kohonen, T.,Self-organization and Associative Memory, 3rd ed., Berlin: Springer-Verlag, 1989.
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.
Burton, R. M., Faris, W. G., A self-organizing cluster process,Ann. of Appl Prob., 1996, 6(4): 1232.
Grossberg, S., Competitive learning: from interactive activation to adaptive resonance cognitive,Science, 1987, 1: 23.
Carpenter, G. A., Grossberg, S., The ART of adaptive pattern recognition by a selforganizing neural network,Trans. IEEE on Computer, 1988, 37(3): 77.
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.
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.
Oja, E., Neural betworks, principle components, and subspace,International Journal of Neural Systems, 1989, 1: 61.
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.
Benveniste, A., Metivier, M., Priouret, P.,Adaptive Algorithm and Stochastic Approximations, Berlin: Springer, 1990.
Chen, H. F., Zhu, Y. M.,Stochastic Approximations (in Chinese), Shanghai: Shanghai Science and Technology Press, 1996.
Kunsch, H., Geman, S., Kehagias, A., Hidden Markov random fields,Ann. Appl. Probab., 1993, 3(3): 577.
Rabiner, L. R., A tutorial on hidden Markov models and selected applications in speech recognition, inProc. IEEE, 1989, 77(2): 267.
Rabiner, L. R., Juang Biing-hwang,Fundamentals of Speech Recognition, Hong Kong: Prince Hall International Inc., 1993.
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.
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.
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.
Leroux, B. G., Maximum-likelihood estimation for hidden Markov modeling,Stoc. Processes and their Appl., 1992, 40(1): 127.
Elliott, R. J., Aggoun, L., Moore, J. B.,Hidden Markov Models, Berlin: Springer-Verlag, 1995.
Ho Yu-chi Larry, Soft Optimization of Hard Problem, inProc. of International Conference on Control and Information (invited talk), Hong Kong, 1996.
Author information
Authors and Affiliations
About this article
Cite this article
Qian, M., Gong, G. Computational intelligence: From mathematical point of view. Chin. Sci. Bull. 44, 865–880 (1999). https://doi.org/10.1007/BF02885056
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02885056