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A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data

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  • Makoto Aoshima
  • Kazuyoshi Yata

Abstract

In this paper, we consider a scale adjusted-type distance-based classifier for high-dimensional data. We first give such a classifier that can ensure high accuracy in misclassification rates for two-class classification. We show that the classifier is not only consistent but also asymptotically normal for high-dimensional data. We provide sample size determination so that misclassification rates are no more than a prespecified value. We propose a classification procedure called the misclassification rate adjusted classifier. We further develop the classifier to multiclass classification. We show that the classifier can still enjoy asymptotic properties and ensure high accuracy in misclassification rates for multiclass classification. Finally, we demonstrate the proposed classifier in actual data analyses by using a microarray data set. Copyright The Institute of Statistical Mathematics, Tokyo 2014

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  • Makoto Aoshima & Kazuyoshi Yata, 2014. "A distance-based, misclassification rate adjusted classifier for multiclass, high-dimensional data," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(5), pages 983-1010, October.
    • Handle: RePEc:spr:aistmt:v:66:y:2014:i:5:p:983-1010
    DOI: 10.1007/s10463-013-0435-8
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    5. Yata, Kazuyoshi & Aoshima, Makoto, 2013. "Correlation tests for high-dimensional data using extended cross-data-matrix methodology," Journal of Multivariate Analysis, Elsevier, vol. 117(C), pages 313-331.
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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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    Citations

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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. 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.
    3. Kazuyoshi Yata & Makoto Aoshima, 2020. "Geometric consistency of principal component scores for high‐dimensional mixture models and its application," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 899-921, September.
    4. Ishii, Aki & Yata, Kazuyoshi & Aoshima, Makoto, 2022. "Geometric classifiers for high-dimensional noisy data," Journal of Multivariate Analysis, Elsevier, vol. 188(C).
    5. Hyodo, Masashi & Watanabe, Hiroki & Seo, Takashi, 2018. "On simultaneous confidence interval estimation for the difference of paired mean vectors in high-dimensional settings," Journal of Multivariate Analysis, Elsevier, vol. 168(C), pages 160-173.
    6. Marron, J.S., 2017. "Big Data in context and robustness against heterogeneity," Econometrics and Statistics, Elsevier, vol. 2(C), pages 73-80.
    7. Rauf Ahmad, M. & Pavlenko, Tatjana, 2018. "A U-classifier for high-dimensional data under non-normality," Journal of Multivariate Analysis, Elsevier, vol. 167(C), pages 269-283.
    8. 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.
    9. 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).
    10. Makoto Aoshima & Kazuyoshi Yata, 2019. "High-Dimensional Quadratic Classifiers in Non-sparse Settings," Methodology and Computing in Applied Probability, Springer, vol. 21(3), pages 663-682, September.
    11. 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).

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