Upper-bound estimates for classifiers based on a dissimilarity function
- 50 Downloads
Approaches to calculating upper-bound estimates of recognition probability are proposed that can be used for a more general class of models. One of estimates determines the stability of object coverage by classification algorithms on the basis of distribution of distances between objects, and another estimate is underlain by leave-one-out cross-validation. This considerably simplifies and facilitates the construction of estimates.
Keywordsupper-bound estimate for recognition probability leave-one-out cross-validation (LOOCV) stability of object coverage by classification algorithms distribution of distances right (left) asymmetry metric, class of objects
Unable to display preview. Download preview PDF.
- 1.K. V. Vorontsov, “Combinatorial probability and the tightness of generalization bounds,” Pattern Recognition and Image Analysis, 18, No. 2, 243–259 (2008).Google Scholar
- 3.Yu. I. Zhuravlev, “An algebraic approach to recognition or classification problems,” Problems of Cybernetics, 33, 5–68 (1978).Google Scholar
- 4.K. V. Vorontsov, Machine Learning and Data Analysis: A Series of Lectures “Mathematical methods of learning from precedents,” http://www.ccas.ru/voron/teaching.html.
- 5.M. Shlezinger and V. Glavach, Ten Lectures on Statistical and Structural Recognition [in Russian], Naukova Dumka, Kiev (2004).Google Scholar
- 6.T. K. Moon and W. C. Stirling, Mathematical Methods and Algorithms for Signal Processing, Prentice-Hall, N.Y. (2000).Google Scholar
- 7.B. E. Kapustii, B. P. Rusyn, and V. A. Tayanov, “Classifier optimization in small sample size condition,” Automatic Control and Computer Sci., 40, No. 5, 17–22 (2006).Google Scholar
- 8.B. O. Kapustii, B. P. Rusyn, and V. A. Tayanov, “Combinatorial estimation of the influence of a class information coverage reduction on the generalization ability of 1NN classification algorithms,” Artificial Intelligence, No. 1, 49–54 (2008).Google Scholar
- 9.S. Karlin, Fundamentals of the Theory of Random Processes [Russian translation], Mir, Moscow (1971).Google Scholar
- 10.V. S. Korolyuk, N. I. Portenko, A. V. Skorokhod, and A. F. Turbin, A Manual on Probability Theory and Mathematical Statistics [in Russian], Nauka, Moscow (1985).Google Scholar
- 11.C. M. Bishop, Pattern Recognition and Machine Learning (Information Science and Statistics), Springer, London (2006).Google Scholar
- 12.E. W. Weisstein, Chebyshev inequality, http://mathworld.wolfram.com/Chebyshev Inequality.html, 10.12.2008.
- 13.E. W. Weisstein, Gauss inequality, http://mathworld.wolfram.com/GaussInequality.html, 10.12.2008.
- 14.G. Tu. and R. Gonsales, Principles of Pattern Recognition [Russian translation], Mir, Moscow (1978).Google Scholar
- 15.B. O. Kapustii, B. P. Rusyn, and V. A. Tayanov, “A new approach to the definition of the probability of correct recognition of objects from sets,” USiM, No. 2, 8–13 (2005).Google Scholar