Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability

Nicholas A. Nechval; Konstantin N. Nechval

doi:doi:10.11648/j.ajtas.s.2016050201.12

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Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability

Nicholas A. Nechval, Konstantin N. Nechval

Published in American Journal of Theoretical and Applied Statistics (Volume 5, Issue 2-1)

Received: 9 September 2015 Accepted: 10 September 2015 Published: 30 November 2015

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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.

Published in	American Journal of Theoretical and Applied Statistics (Volume 5, Issue 2-1) This article belongs to the Special Issue Novel Ideas for Efficient Optimization of Statistical Decisions and Predictive Inferences under Parametric Uncertainty of Underlying Models with Applications
DOI	10.11648/j.ajtas.s.2016050201.12
Page(s)	7-11
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2015. Published by Science Publishing Group

Keywords

Pattern, Recognition, Classification, Misclassification, Probability, Minimization

References

[1]	R. Fisher, “The use of multiple measurements in taxonomic problems,” Ann. Eugenics, vol. 7, pp. 178 188, 1936.
[2]	K. V. Mardia, J. T. Kent, and J. M. Bibby, Multivariate Analysis. Academic Press, 1979.
[3]	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.
[4]	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.
[5]	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.
[6]	R. O. Duda, P. E. Hart, and D. G. Stork, Pattern classification. New York: Wiley. (Second Edition.), 2001.
[7]	S. T. John and C. Nello, Kernel Methods for Pattern Analysis. Cambridge: Cambridge University Press, 2004.
[8]	A. C. Rencher, Methods of Multivariate Analysis. John Wiley & Sons. (Second Edition.), 2002.
[9]	T. Sergios and K. Konstantinos, Pattern Recognition. Singapore: Elsevier Ltd. (Third Edition.), 2006.
[10]	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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APA Style

Nicholas A. Nechval, Konstantin N. Nechval. (2015). Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability. American Journal of Theoretical and Applied Statistics, 5(2-1), 7-11. https://doi.org/10.11648/j.ajtas.s.2016050201.12

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ACS Style

Nicholas A. Nechval; Konstantin N. Nechval. Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability. Am. J. Theor. Appl. Stat. 2015, 5(2-1), 7-11. doi: 10.11648/j.ajtas.s.2016050201.12

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AMA Style

Nicholas A. Nechval, Konstantin N. Nechval. Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability. Am J Theor Appl Stat. 2015;5(2-1):7-11. doi: 10.11648/j.ajtas.s.2016050201.12

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@article{10.11648/j.ajtas.s.2016050201.12,
  author = {Nicholas A. Nechval and Konstantin N. Nechval},
  title = {Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {2-1},
  pages = {7-11},
  doi = {10.11648/j.ajtas.s.2016050201.12},
  url = {https://doi.org/10.11648/j.ajtas.s.2016050201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2016050201.12},
  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.},
 year = {2015}
}

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TY  - JOUR
T1  - Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability
AU  - Nicholas A. Nechval
AU  - Konstantin N. Nechval
Y1  - 2015/11/30
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DO  - 10.11648/j.ajtas.s.2016050201.12
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AB  - 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.
VL  - 5
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Author Information

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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APA Style

Nicholas A. Nechval, Konstantin N. Nechval. (2015). Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability. American Journal of Theoretical and Applied Statistics, 5(2-1), 7-11. https://doi.org/10.11648/j.ajtas.s.2016050201.12

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ACS Style

Nicholas A. Nechval; Konstantin N. Nechval. Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability. Am. J. Theor. Appl. Stat. 2015, 5(2-1), 7-11. doi: 10.11648/j.ajtas.s.2016050201.12

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AMA Style

Nicholas A. Nechval, Konstantin N. Nechval. Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability. Am J Theor Appl Stat. 2015;5(2-1):7-11. doi: 10.11648/j.ajtas.s.2016050201.12

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@article{10.11648/j.ajtas.s.2016050201.12,
  author = {Nicholas A. Nechval and Konstantin N. Nechval},
  title = {Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {5},
  number = {2-1},
  pages = {7-11},
  doi = {10.11648/j.ajtas.s.2016050201.12},
  url = {https://doi.org/10.11648/j.ajtas.s.2016050201.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.s.2016050201.12},
  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.},
 year = {2015}
}

Copy | Download

TY  - JOUR
T1  - Efficient Approach to Pattern Recognition Based on Minimization of Misclassification Probability
AU  - Nicholas A. Nechval
AU  - Konstantin N. Nechval
Y1  - 2015/11/30
PY  - 2015
N1  - https://doi.org/10.11648/j.ajtas.s.2016050201.12
DO  - 10.11648/j.ajtas.s.2016050201.12
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 7
EP  - 11
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.s.2016050201.12
AB  - 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.
VL  - 5
IS  - 2-1
ER  -

Copy | Download