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Regularized classification for mixed continuous and categorical variables under across-location heteroscedasticity

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  • Leung, Chi-Ying

Abstract

A regularized classifier is proposed for a two-population classification problem of mixed continuous and categorical variables in a general location model(GLOM). The limiting overall expected error for the classifier is given. It can be used in an optimization search for the regularization parameters. For a heteroscedastic spherical dispersion across all locations, an asymptotic error is available which provides an alternative criterion for the optimization search. In addition, the asymptotic error can serve as a baseline for practical comparisons with other classifiers. Results based on a simulation and two real datasets are presented.

Suggested Citation

  • Leung, Chi-Ying, 2005. "Regularized classification for mixed continuous and categorical variables under across-location heteroscedasticity," Journal of Multivariate Analysis, Elsevier, vol. 93(2), pages 358-374, April.
    • Handle: RePEc:eee:jmvana:v:93:y:2005:i:2:p:358-374
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    References listed on IDEAS

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    1. Leung, Chi-Ying, 1996. "The location linear discriminant for classifying observations with unequal variances," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 23-29, December.
    2. W. Krzanowski, 1993. "The location model for mixtures of categorical and continuous variables," Journal of Classification, Springer;The Classification Society, vol. 10(1), pages 25-49, January.
    3. Chi-Ying Leung, 1998. "The Covariance Adjusted Location Linear Discriminant Function for Classifying Data with Unequal Dispersion Matrices in Different Locations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 417-431, September.
    4. Yin, Y. Q., 1986. "Limiting spectral distribution for a class of random matrices," Journal of Multivariate Analysis, Elsevier, vol. 20(1), pages 50-68, October.
    5. LaDue, Eddy L. & Bowne, Doug & Kurdieh, Zaid & Oostveen, Carry & Staehr, A. Edward & Radick, Charles Z. & Hilts, Jacqueline M. & Baase, Karen & Karszes, Jason & Putnam, Linda D., 2000. "Dairy Farm Business Summary, Central Valleys Region, 1999," EB Series 122296, Cornell University, Department of Applied Economics and Management.
    6. 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.
    7. Leung, Chi-Ying, 2003. "The effect of across-location heteroscedasticity on the classification of mixed categorical and continuous data," Journal of Multivariate Analysis, Elsevier, vol. 84(2), pages 369-386, February.
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