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A plug-in approach to sparse and robust principal component analysis

Author

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  • Luca Greco

    (University of Sannio)

  • Alessio Farcomeni

    (Sapienza, University of Rome)

Abstract

We propose a method for sparse and robust principal component analysis. The methodology is structured in two steps: first, a robust estimate of the covariance matrix is obtained, then this estimate is plugged-in into an elastic-net regression which enforces sparseness. Our approach provides an intuitive, general and flexible extension of sparse principal component analysis to the robust setting. We also show how to implement the algorithm when the dimensionality exceeds the number of observations by adapting the approach to the use of robust loadings from ROBPCA. The proposed technique is seen to compare well for simulated and real datasets.

Suggested Citation

  • Luca Greco & Alessio Farcomeni, 2016. "A plug-in approach to sparse and robust principal component analysis," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 25(3), pages 449-481, September.
    • Handle: RePEc:spr:testjl:v:25:y:2016:i:3:d:10.1007_s11749-015-0464-0
    DOI: 10.1007/s11749-015-0464-0
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    References listed on IDEAS

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    1. Alessio Farcomeni, 2009. "An exact approach to sparse principal component analysis," Computational Statistics, Springer, vol. 24(4), pages 583-604, December.
    2. N. Locantore & J. Marron & D. Simpson & N. Tripoli & J. Zhang & K. Cohen & Graciela Boente & Ricardo Fraiman & Babette Brumback & Christophe Croux & Jianqing Fan & Alois Kneip & John Marden & Daniel P, 1999. "Robust principal component analysis for functional data," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 8(1), pages 1-73, June.
    3. Salibian-Barrera, Matias & Van Aelst, Stefan & Willems, Gert, 2006. "Principal Components Analysis Based on Multivariate MM Estimators With Fast and Robust Bootstrap," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1198-1211, September.
    4. Cerioli, Andrea & Farcomeni, Alessio, 2011. "Error rates for multivariate outlier detection," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 544-553, January.
    5. Hui Zou & Trevor Hastie, 2005. "Addendum: Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(5), pages 768-768, November.
    6. Croux, Christophe & Ruiz-Gazen, Anne, 2005. "High breakdown estimators for principal components: the projection-pursuit approach revisited," Journal of Multivariate Analysis, Elsevier, vol. 95(1), pages 206-226, July.
    7. Hui Zou & Trevor Hastie, 2005. "Regularization and variable selection via the elastic net," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(2), pages 301-320, April.
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    Cited by:

    1. Daniel Fraiman & Nicolas Fraiman & Ricardo Fraiman, 2017. "Nonparametric statistics of dynamic networks with distinguishable nodes," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 26(3), pages 546-573, September.
    2. Luca Greco & Antonio Lucadamo & Pietro Amenta, 2020. "An Impartial Trimming Approach for Joint Dimension and Sample Reduction," Journal of Classification, Springer;The Classification Society, vol. 37(3), pages 769-788, October.
    3. Trucíos, Carlos & Hotta, Luiz K. & Valls Pereira, Pedro L., 2019. "On the robustness of the principal volatility components," Journal of Empirical Finance, Elsevier, vol. 52(C), pages 201-219.
    4. Claudio Agostinelli & Luca Greco, 2019. "Weighted likelihood estimation of multivariate location and scatter," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 756-784, September.

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