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Distance-based classifier by data transformation for high-dimension, strongly spiked eigenvalue models

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  • Makoto Aoshima

    (University of Tsukuba)

  • Kazuyoshi Yata

    (University of Tsukuba)

Abstract

We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data often have the SSE model. We consider a distance-based classifier using eigenstructures for the SSE model. We apply the noise-reduction methodology to estimation of the eigenvalues and eigenvectors in the SSE model. We create a new distance-based classifier by transforming data from the SSE model to the non-SSE model. We give simulation studies and discuss the performance of the new classifier. Finally, we demonstrate the new classifier by using microarray data sets.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:71:y:2019:i:3:d:10.1007_s10463-018-0655-z
    DOI: 10.1007/s10463-018-0655-z
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    References listed on IDEAS

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    4. Yata, Kazuyoshi & Aoshima, Makoto, 2013. "PCA consistency for the power spiked model in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 122(C), pages 334-354.
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    8. 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.
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    10. Yata, Kazuyoshi & Aoshima, Makoto, 2010. "Effective PCA for high-dimension, low-sample-size data with singular value decomposition of cross data matrix," Journal of Multivariate Analysis, Elsevier, vol. 101(9), pages 2060-2077, October.
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    Cited by:

    1. Yugo Nakayama & Kazuyoshi Yata & Makoto Aoshima, 2020. "Bias-corrected support vector machine with Gaussian kernel in high-dimension, low-sample-size settings," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 72(5), pages 1257-1286, October.
    2. 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).
    3. Liebscher, Eckhard & Okhrin, Ostap, 2023. "Semiparametric estimation of the high-dimensional elliptical distribution," Journal of Multivariate Analysis, Elsevier, vol. 195(C).
    4. Ishii, Aki & Yata, Kazuyoshi & Aoshima, Makoto, 2022. "Geometric classifiers for high-dimensional noisy data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Nakayama, Yugo & Yata, Kazuyoshi & Aoshima, Makoto, 2021. "Clustering by principal component analysis with Gaussian kernel in high-dimension, low-sample-size settings," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    6. Aki Ishii & Kazuyoshi Yata & Makoto Aoshima, 2021. "Hypothesis tests for high-dimensional covariance structures," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(3), pages 599-622, June.

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