Volume 5, Issue 2-1, March 2016, Page: 7-11
Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability
Nicholas A. Nechval, Department of Mathematics, Baltic International Academy, Riga, Latvia
Konstantin N. Nechval, Department of Applied Mathematics, Transport and Telecommunication Institute, Riga, Latvia
Received: Sep. 9, 2015;       Accepted: Sep. 10, 2015;       Published: Nov. 30, 2015
DOI: 10.11648/j.ajtas.s.2016050201.12      View  3341      Downloads  74
Abstract
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.
Keywords
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
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