Some approaches to pattern recognition problems. (English. Russian original) Zbl 1154.68484
Cybern. Syst. Anal. 43, No. 6, 810-821 (2007); translation from Kibern. Sist. Anal. 2007, No. 6, 55-69 (2007).
Summary: A new approach to selecting the Gibbs distribution in models of objects to be recognized is proposed. This approach proposes to determine the lower and upper bounds for probabilities of the object under study. The distance between these bounds may be used as a measure of error in pattern recognition problems.
MSC:
| 68T10 | Pattern recognition, speech recognition |
Keywords:
Gibbs models of objects; pattern recognition; Bayesian estimate; optimization; upper bound; cumulative distribution functionReferences:
| [1] | G. L. Gimmel’farb and A. V. Zalesnyi, ”Bayesian segmentation of maps using models of the Markov fields given by Gibbs distributions,” in: Abstracts of 3rd All-Union Conf. on Automated Image Processing Systems [in Russian], Leningrad (1989), pp. 22–23. |
| [2] | A. V. Zalesnyi, ”Digital image processing algorithms for images described by Markov random fields,” Author’s Abstracts of PhD Thesis [in Russian], V. M. Glushkov Inst. of Cybernetics AS USSR, Kyiv (1991). |
| [3] | M. I. Schlesinger and V. Hlavac, ”Ten lectures on statistical and structural pattern recognition,” in: Computational Imaging and Vision, Kluwer Acad. Publ., Dordrecht-Boston-London (2002). |
| [4] | P. S. Knopov, ”Markov fields and their application in economics,” Obchysl. Prykl. Matem., 80, 33–46 (1996). · Zbl 0936.60049 |
| [5] | G. Daduna, P. S. Knopov, and P. K. Chornei, ”Local control of Markovian processes of interaction on a graph with a compact set of states,” Cybern. Syst. Analysis, 37, No. 3, 348–360 (2001). · Zbl 1038.93087 · doi:10.1023/A:1011985609994 |
| [6] | T. Liggett, Interacting Particle Systems, Springer-Verlag, New York (1989). · Zbl 0679.60093 |
| [7] | N. B. Vasil’ev and O. K. Kozlov, ”Reversible Markov chains with local interaction,” in: Multicomponent Random Systems [in Russian], Nauka, Moscow (1978), pp. 83–100. |
| [8] | M. B. Averintsev, ”Description of Markov random fields using Gibbs conditional probabilities,” Teor. Veroyatn. Primen., 17, 21–35 (1972). |
| [9] | H. Jeffreys, Theory of Probability, Clarendon Press, Oxford (1961). · Zbl 0116.34904 |
| [10] | E. T. Jaynes, ”Prior probabilities,” IEEE Trans. System Sci. Cybern., SSC-4, 227–241 (1968). · Zbl 0181.21901 · doi:10.1109/TSSC.1968.300117 |
| [11] | J. J. Deeley, M. S. Tierney, and W. J. Zimmer, ”On the usefulness of the maximum entropy principle in the Bayesian estimation of reliability,” IEEE Trans. on Reliability, R-19, 110–115 (1970). · doi:10.1109/TR.1970.5216416 |
| [12] | V. P. Savchuk and H. F. Martz, ”Bayes reliability estimation using multiple sources of prior information: binomial sampling,” IEEE Trans. on Reliability, 138–144 (1994). |
| [13] | H. F. Martz and R. A. Waller, Bayesian Reliability Analysis, Krieger Publ. Co., Malabar, Florida (1991). · Zbl 0763.62053 |
| [14] | Mosleh G. Apostolakis, ”Some properties of distributions useful in the study of rare events,” IEEE Trans. on Reliability, R-31, 87–94 (1982). · Zbl 0481.60084 · doi:10.1109/TR.1982.5221242 |
| [15] | H. Robins, ”Asymptotically sub-minimax solutions to compound statistical decision problems,” Proc. 2nd Berkeley Symp. Math. Stat. Probab., University of California Press, Berkeley (1951). |
| [16] | J. O. Berger, ”The robust Bayesian viewpoint (with discussion),” in: J. Kadane (ed.), Robustness of Bayesian Analysis, North Holland, Amsterdam (1995). |
| [17] | B. Vidakovic, ”Gamma-minimax: A paradigm for conservative robust Bayesians,” in: Rios and Ruggeri (eds.), Robustness of Bayesian Inference, Lecture Notes in Statistics, Springer Verlag, 152 (2000), pp. 241–259. · Zbl 1281.62040 |
| [18] | F. Ruggeri and S. Sivaganesan, ”On a global sensitivity measure for Bayesian inference,” Sankhya: The Indian J. of Statistics, 62, Series A, Pt. 1, 110–127 (2000). · Zbl 0973.62027 |
| [19] | C. Carota and F. Ruggeri, ”Robust Bayesian analysis given priors on partition sets,” Test, 3, No. 2, 73–86 (1994). · Zbl 0812.62034 · doi:10.1007/BF02562694 |
| [20] | J. O. Berger, ”An overview of robust Bayesian analysis (with comments),” Test, 3, No. 1, 51–24 (1994). · Zbl 0827.62026 · doi:10.1007/BF02562676 |
| [21] | A. Golodnikov, P. Knopov, P. Pardalos, and S. Uryasev, ”Optimization in the space of distribution functions and applications in the Bayes analysis,” in: Probabilistic Constrained Optimization: Methodology and Applications, Kluwer Acad. Publ. (2000), pp. 102–131. · Zbl 1052.90592 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
