IDEAS home Printed from https://ideas.repec.org/a/spr/compst/v33y2018i4d10.1007_s00180-018-0826-7.html
   My bibliography  Save this article

Stability approach to selecting the number of principal components

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00180-018-0826-7
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00180-018-0826-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Besse, Philippe, 1992. "PCA stability and choice of dimensionality," Statistics & Probability Letters, Elsevier, vol. 13(5), pages 405-410, April.
    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. Lexin Li, 2007. "Sparse sufficient dimension reduction," Biometrika, Biometrika Trust, vol. 94(3), pages 603-613.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Adrian O’Hagan & Arthur White, 2019. "Improved model-based clustering performance using Bayesian initialization averaging," Computational Statistics, Springer, vol. 34(1), pages 201-231, March.
    2. Changrong Yan & Dixin Zhang, 2013. "Sparse dimension reduction for survival data," Computational Statistics, Springer, vol. 28(4), pages 1835-1852, August.
    3. Heng-Hui Lue, 2015. "An Inverse-regression Method of Dependent Variable Transformation for Dimension Reduction with Non-linear Confounding," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(3), pages 760-774, September.
    4. Sauvenier, Mathieu & Van Bellegem, Sébastien, 2023. "Direction Identification and Minimax Estimation by Generalized Eigenvalue Problem in High Dimensional Sparse Regression," LIDAM Discussion Papers CORE 2023005, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    5. Bilin Zeng & Xuerong Meggie Wen & Lixing Zhu, 2017. "A link-free sparse group variable selection method for single-index model," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(13), pages 2388-2400, October.
    6. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    7. Hung Hung & Su‐Yun Huang, 2019. "Sufficient dimension reduction via random‐partitions for the large‐p‐small‐n problem," Biometrics, The International Biometric Society, vol. 75(1), pages 245-255, March.
    8. Marek Śmieja & Magdalena Wiercioch, 2017. "Constrained clustering with a complex cluster structure," 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. 11(3), pages 493-518, September.
    9. Hojin Yang & Hongtu Zhu & Joseph G. Ibrahim, 2018. "MILFM: Multiple index latent factor model based on high‐dimensional features," Biometrics, The International Biometric Society, vol. 74(3), pages 834-844, September.
    10. Wang, Pei & Yin, Xiangrong & Yuan, Qingcong & Kryscio, Richard, 2021. "Feature filter for estimating central mean subspace and its sparse solution," Computational Statistics & Data Analysis, Elsevier, vol. 163(C).
    11. Wang, Qin & Xue, Yuan, 2021. "An ensemble of inverse moment estimators for sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    12. Jianqing Fan & Jinchi Lv, 2008. "Sure independence screening for ultrahigh dimensional feature space," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 70(5), pages 849-911, November.
    13. Wang, Qin & Yin, Xiangrong, 2008. "A nonlinear multi-dimensional variable selection method for high dimensional data: Sparse MAVE," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4512-4520, May.
    14. Yoo, Jae Keun, 2013. "Advances in seeded dimension reduction: Bootstrap criteria and extensions," Computational Statistics & Data Analysis, Elsevier, vol. 60(C), pages 70-79.
    15. Shin, Seung Jun & Artemiou, Andreas, 2017. "Penalized principal logistic regression for sparse sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 111(C), pages 48-58.
    16. Dray, Stephane, 2008. "On the number of principal components: A test of dimensionality based on measurements of similarity between matrices," Computational Statistics & Data Analysis, Elsevier, vol. 52(4), pages 2228-2237, January.
    17. Moradi Rekabdarkolaee, Hossein & Wang, Qin, 2017. "Variable selection through adaptive MAVE," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 44-51.
    18. Fang, Fang & Yu, Zhou, 2020. "Model averaging assisted sufficient dimension reduction," Computational Statistics & Data Analysis, Elsevier, vol. 152(C).
    19. Yu, Zhou & Dong, Yuexiao & Huang, Mian, 2014. "General directional regression," Journal of Multivariate Analysis, Elsevier, vol. 124(C), pages 94-104.
    20. Zou, Changliang & Chen, Xin, 2012. "On the consistency of coordinate-independent sparse estimation with BIC," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 248-255.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:compst:v:33:y:2018:i:4:d:10.1007_s00180-018-0826-7. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.