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Stability approach to selecting the number of principal components

Author

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  • Jiyeon Song

    (Korea University)

  • Seung Jun Shin

    (Korea University)

Abstract

Principal component analysis (PCA) is a canonical tool that reduces data dimensionality by finding linear transformations that project the data into a lower dimensional subspace while preserving the variability of the data. Selecting the number of principal components (PC) is essential but challenging for PCA since it represents an unsupervised learning problem without a clear target label at the sample level. In this article, we propose a new method to determine the optimal number of PCs based on the stability of the space spanned by PCs. A series of analyses with both synthetic data and real data demonstrates the superior performance of the proposed method.

Suggested Citation

  • Jiyeon Song & Seung Jun Shin, 2018. "Stability approach to selecting the number of principal components," Computational Statistics, Springer, vol. 33(4), pages 1923-1938, December.
    • Handle: RePEc:spr:compst:v:33:y:2018:i:4:d:10.1007_s00180-018-0826-7
    DOI: 10.1007/s00180-018-0826-7
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    References listed on IDEAS

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    1. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    2. Jean-Patrick Baudry & Margarida Cardoso & Gilles Celeux & Maria Amorim & Ana Ferreira, 2015. "Enhancing the selection of a model-based clustering with external categorical variables," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 9(2), pages 177-196, June.
    3. Besse, Philippe, 1992. "PCA stability and choice of dimensionality," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 405-410, April.
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    Cited by:

    1. Armeen Taeb & Parikshit Shah & Venkat Chandrasekaran, 2020. "False discovery and its control in low rank estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 82(4), pages 997-1027, September.

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