Abstract
The MinMax measure of information, defined by Kapur, Baciu and Kesavan [6], is a quantitative measure of the information contained in a given set of moment constraints. It is based on both maximum and minimum entropy. Computational difficulties in the determination of minimum entropy probability distributions (MinEPD) have inhibited exploration of the full potential of minimum entropy and, hence, the MinMax measure. Initial attempts to solve the minimum entropy problem were directed towards finding analytical solutions for some specific set of constraints. Here, we present a numerical solution to the general minimum entropy problem and discuss the significance of minimum entropy and the MinMax measure. Some numerical examples are given for illustration.
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References
H.P. Benson. Concave minimization: Theory, applications and algorithms. In Horst. R. and Pardalos. P.M., editors, Handbook of Global Optimization. Kluwer Academic Publications, 1995.
R. Fletcher. Practical Methods of Optimization. John Wiley, 1991.
R.M. Gray and J.E. Shore. Minimum cross-entropy pattern classification and cluster analysis. IEEE trans. on PAMI, 4 (1): 11–17, 1982.
R. Horst and H. Thy. Global Optimization: Deterministic Approaches. Springer-Verlag, Berlin, 1993.
J.N. Kapur, G. Baciu, and H.K. Kesavan. On the relationship between variance and minimum entropy. Internal publication of Univ. of Waterloo, Waterloo, Canada, 1994.
J.N. Kapur, G. Baciu, and H.K. Kesavan. The minmax information measure. Int. J. Systems Sci., 26 (1): 1–12, 1995.
J.N. Kapur and H.K. Kesavan. Generalized Maximum Entropy Principle (with Applications). Sandford Educational Press, Waterloo, 1989.
J.N. Kapur and H.K. Kesavan. Entropy Optimization Principles with Applications. Academic Press, Inc., New York, 1992.
H.K. Kesavan and G. Baciu. The role of entropy optimization principles in the study of probabilistic systems. Proc. Int. Cony. Cybernatics and Systems(ICCS 93), pages 25–35, 1993.
H.K. Kesavan and L. Yuan. Minimum entropy and information measure. IEEE trans. on SMC, Aug, 1998.
H.K. Kesavan and Q. Zhao. An heuristic approach for finding minimum entropy probability distributions. Internal publication of Univ. of Waterloo, Waterloo, Canada, 1995.
S. Munirathnam. The role of minmax entropy measure in probabilistic systems design. Master’s thesis, University of Waterloo, Waterloo, Ontario, Canada, 1998.
A.T. Phillips and J.B. Rosen. Sufficient conditions for solving linearly constrained separable concave global minimization problems. J. of Global Optimization, 3: 79–94, 1993.
S.D. Pietra, V.D. Pietra, and J. Lafferty. Inducing features of random fields. IEEE trans. on PAMI, 19 (4): 380–393, 1997.
L.E. Scales. Introduction to Non-linear Optimization. Macmillan, London, 1985.
S. Watanabe. Pattern recognition as a quest for minimum entropy. Pattern Recognition, 13: 381–387, 1981.
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Srikanth, M., Kesavan, H.K., Roe, P. (2003). Computation of the MinMax Measure. In: Karmeshu (eds) Entropy Measures, Maximum Entropy Principle and Emerging Applications. Studies in Fuzziness and Soft Computing, vol 119. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-36212-8_13
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DOI: https://doi.org/10.1007/978-3-540-36212-8_13
Publisher Name: Springer, Berlin, Heidelberg
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