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Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings

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  • Nakagawa, Tomoyuki
  • Watanabe, Hiroki
  • Hyodo, Masashi

Abstract

This paper presents a variable selection method for the Euclidean distance-based classifier in high-dimensional settings. We are concerned that the expected probabilities of misclassification (EPMC) for the Euclidean distance-based classifier may be increasing with dimension when redundant variables are included in feature values. First, we show the Euclidean distance-based classifier with only non-redundant variables reduces asymptotic EPMC more than the Euclidean distance-based classifier with all variables. Next, we obtain a kick-one-out based variable selection method that helps reduce EPMC and prove its consistency in variable selection in the context of high dimensionality. Finally, we conduct a Monte Carlo simulation study to examine the finite sample performance of the proposed selection method. Our simulation results show that the selection method frequently selects the set containing non-redundant variables. We also observed that the discrimination rules constructed from the selected variables reduce EPMC more than the discrimination rules constructed from all variables.

Suggested Citation

  • Nakagawa, Tomoyuki & Watanabe, Hiroki & Hyodo, Masashi, 2021. "Kick-one-out-based variable selection method for Euclidean distance-based classifier in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 184(C).
    • Handle: RePEc:eee:jmvana:v:184:y:2021:i:c:s0047259x21000348
    DOI: 10.1016/j.jmva.2021.104756
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    References listed on IDEAS

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    1. Makoto Aoshima & Kazuyoshi Yata, 2019. "Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 71(3), pages 473-503, June.
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    6. 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.
    7. Fujikoshi, Yasunori, 1985. "Selection of variables in two-group discriminant analysis by error rate and Akaike's information criteria," Journal of Multivariate Analysis, Elsevier, vol. 17(1), pages 27-37, August.
    8. Hyodo, Masashi & Kubokawa, Tatsuya, 2014. "A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 364-379.
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