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Nonparametric classification of high dimensional observations

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  • Reza Modarres

    (George Washington University)

Abstract

We consider the nonparametric classification of high dimensional, low sample size (HDLSS) data where the classical discrimination methods break down due to the singularity of the sample covariance matrix. We present new dissimilarity indices, discuss their asymptotic properties in the HDLSS setting, use them in building powerful classifiers, and compare their behavior with existing methods. We illustrate the difficulties with the Euclidean nearest neighbor method and prove that dissimilarity-based classifiers produce misclassification rates that tend to zero as $$p\rightarrow \infty $$ p → ∞ . We present test-based classifiers in the HDLSS setting. A simulation study compares the misclassification rates of diagonal linear discriminant analysis with twelve other nonparametric classifiers. The methods are applied to microarray data for classification of prostate cancer.

Suggested Citation

  • Reza Modarres, 2023. "Nonparametric classification of high dimensional observations," Statistical Papers, Springer, vol. 64(6), pages 1833-1859, December.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:6:d:10.1007_s00362-022-01363-3
    DOI: 10.1007/s00362-022-01363-3
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    References listed on IDEAS

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    1. Modarres, Reza, 2022. "A high dimensional dissimilarity measure," Computational Statistics & Data Analysis, Elsevier, vol. 175(C).
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