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Minimum distance classification rules for high dimensional data

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  • Srivastava, Muni S.

Abstract

In this article, the problem of classifying a new observation vector into one of the two known groups [Pi]i,i=1,2, distributed as multivariate normal with common covariance matrix is considered. The total number of observation vectors from the two groups is, however, less than the dimension of the observation vectors. A sample-squared distance between the two groups, using Moore-Penrose inverse, is introduced. A classification rule based on the minimum distance is proposed to classify an observation vector into two or several groups. An expression for the error of misclassification when there are only two groups is derived for large p and n=O(p[delta]),0

Suggested Citation

  • Srivastava, Muni S., 2006. "Minimum distance classification rules for high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 97(9), pages 2057-2070, October.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:9:p:2057-2070
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    References listed on IDEAS

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    2. Saranadasa, H., 1993. "Asymptotic Expansion of the Misclassification Probabilities of D- and A-Criteria for Discrimination from Two High Dimensional Populations Using the Theory of Large Dimensional Random Matrices," Journal of Multivariate Analysis, Elsevier, vol. 46(1), pages 154-174, July.
    3. J. D. Wilbur & J. K. Ghosh & C. H. Nakatsu & S. M. Brouder & R. W. Doerge, 2002. "Variable Selection in High-Dimensional Multivariate Binary Data with Application to the Analysis of Microbial Community DNA Fingerprints," Biometrics, The International Biometric Society, vol. 58(2), pages 378-386, June.
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    Cited by:

    1. Yata, Kazuyoshi & Aoshima, Makoto, 2012. "Effective PCA for high-dimension, low-sample-size data with noise reduction via geometric representations," Journal of Multivariate Analysis, Elsevier, vol. 105(1), pages 193-215.
    2. Amitrajeet A. Batabyal & Hamid Beladi, 2015. "Optimal Transport Provision To A Tourist Destination: A Mechanism Design Approach," Working Papers 0140eco, College of Business, University of Texas at San Antonio.
    3. Kubokawa, Tatsuya & Hyodo, Masashi & Srivastava, Muni S., 2013. "Asymptotic expansion and estimation of EPMC for linear classification rules in high dimension," Journal of Multivariate Analysis, Elsevier, vol. 115(C), pages 496-515.
    4. Watanabe, Hiroki & Hyodo, Masashi & Seo, Takashi & Pavlenko, Tatjana, 2015. "Asymptotic properties of the misclassification rates for Euclidean Distance Discriminant rule in high-dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 234-244.
    5. Tatsuya Kubokawa & Masashi Hyodo & Muni S. Srivastava, 2011. "Asymptotic Expansion and Estimation of EPMC for Linear Classification Rules in High Dimension," CIRJE F-Series CIRJE-F-818, CIRJE, Faculty of Economics, University of Tokyo.

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