Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability
American Journal of Theoretical and Applied Statistics
Volume 5, Issue 2-1, March 2016, Pages: 7-11
Received: Sep. 9, 2015; Accepted: Sep. 10, 2015; Published: Nov. 30, 2015
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Nicholas A. Nechval, Department of Mathematics, Baltic International Academy, Riga, Latvia
Konstantin N. Nechval, Department of Applied Mathematics, Transport and Telecommunication Institute, Riga, Latvia
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In this paper, an efficient approach to pattern recognition (classification) is suggested. It is based on minimization of misclassification probability and uses transition from high dimensional problem (dimension p≥2) to one dimensional problem (dimension p=1) in the case of the two classes as well as in the case of several classes with separation of classes as much as possible. The probability of misclassification, which is known as the error rate, is also used to judge the ability of various pattern recognition (classification) procedures to predict group membership. The approach does not require the arbitrary selection of priors as in the Bayesian classifier and represents the novel pattern recognition (classification) procedure that allows one to take into account the cases, which are not adequate for Fisher’s classification rule (i.e., the distributions of the classes are not multivariate normal or covariance matrices of those are different or there are strong multi-nonlinearities). Moreover, it also allows one to classify a set of multivariate observations, where each of the observations belongs to the same unknown class. For the cases, which are adequate for Fisher’s classification rule, the proposed approach gives the results similar to that of Fisher’s classification rule. For illustration, practical examples are given.
Pattern, Recognition, Classification, Misclassification, Probability, Minimization
To cite this article
Nicholas A. Nechval, Konstantin N. Nechval, Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability, American Journal of Theoretical and Applied Statistics. Special Issue: Novel Ideas for Efficient Optimization of Statistical Decisions and Predictive Inferences under Parametric Uncertainty of Underlying Models with Applications. Vol. 5, No. 2-1, 2016, pp. 7-11. doi: 10.11648/j.ajtas.s.2016050201.12
R. Fisher, “The use of multiple measurements in taxonomic problems,” Ann. Eugenics, vol. 7, pp. 178 188, 1936.
K. V. Mardia, J. T. Kent, and J. M. Bibby, Multivariate Analysis. Academic Press, 1979.
N. A. Nechval, K. N. Nechval, and M. Purgailis, “Statistical pattern recognition principles,” in International Encyclopedia of Statistical Science, Part 19, Miodrag Lovric, Ed. Berlin, Heidelberg: Springer-Verlag, 2011, pp. 1453 1457.
N. A. Nechval, K. N. Nechval, M. Purgailis, V. F. Strelchonok, G. Berzins, and M. Moldovan, “New approach to pattern recognition via comparison of maximum separations,” Computer Modelling and New Technologies, vol. 15, pp. 30  40, 2011.
N. A. Nechval, K. N. Nechval, V. Danovich, G. Berzins, “Distance-based approaches to pattern recognition via embedding,” in Lecture Notes in Engineering and Computer Science: Proceedings of The World Congress on Engineering 2014, 24 July, 2014, London, U.K., pp. 759 764.
R. O. Duda, P. E. Hart, and D. G. Stork, Pattern classification. New York: Wiley. (Second Edition.), 2001.
S. T. John and C. Nello, Kernel Methods for Pattern Analysis. Cambridge: Cambridge University Press, 2004.
A. C. Rencher, Methods of Multivariate Analysis. John Wiley & Sons. (Second Edition.), 2002.
T. Sergios and K. Konstantinos, Pattern Recognition. Singapore: Elsevier Ltd. (Third Edition.), 2006.
B. N. Bouma, et al., Evaluation of the detection rate of hemophilia carriers. Statistical Methods for Clinical Decision Making, vol. 7, pp. 339 350, 1975.
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