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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).
    2. Xu, Ping & Brock, Guy N. & Parrish, Rudolph S., 2009. "Modified linear discriminant analysis approaches for classification of high-dimensional microarray data," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1674-1687, March.
    3. Reza Modarres & Yu Song, 2020. "Interpoint distances: Applications, properties, and visualization," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 36(6), pages 1147-1168, November.
    4. Chen, Song Xi & Qin, Yingli, 2010. "A Two Sample Test for High Dimensional Data with Applications to Gene-set Testing," MPRA Paper 59642, University Library of Munich, Germany.
    5. Jeongyoun Ahn & J. S. Marron & Keith M. Muller & Yueh-Yun Chi, 2007. "The high-dimension, low-sample-size geometric representation holds under mild conditions," Biometrika, Biometrika Trust, vol. 94(3), pages 760-766.
    6. Chung Dongjun & Keles Sunduz, 2010. "Sparse Partial Least Squares Classification for High Dimensional Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-32, March.
    7. Yao-Ban Chan & Peter Hall, 2009. "Scale adjustments for classifiers in high-dimensional, low sample size settings," Biometrika, Biometrika Trust, vol. 96(2), pages 469-478.
    8. Biswas, Munmun & Ghosh, Anil K., 2014. "A nonparametric two-sample test applicable to high dimensional data," Journal of Multivariate Analysis, Elsevier, vol. 123(C), pages 160-171.
    9. Liao, Shu-Min & Akritas, Michael, 2007. "Test-based classification: A linkage between classification and statistical testing," Statistics & Probability Letters, Elsevier, vol. 77(12), pages 1269-1281, July.
    10. Tatjana Lange & Karl Mosler & Pavlo Mozharovskyi, 2014. "Fast nonparametric classification based on data depth," Statistical Papers, Springer, vol. 55(1), pages 49-69, February.
    11. Song Huang & Tiejun Tong & Hongyu Zhao, 2010. "Bias-Corrected Diagonal Discriminant Rules for High-Dimensional Classification," Biometrics, The International Biometric Society, vol. 66(4), pages 1096-1106, December.
    12. Marco Marozzi & Amitava Mukherjee & Jan Kalina, 2020. "Interpoint distance tests for high-dimensional comparison studies," Journal of Applied Statistics, Taylor & Francis Journals, vol. 47(4), pages 653-665, March.
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