IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v109y2017icp144-158.html
   My bibliography  Save this article

Bayesian robust principal component analysis with structured sparse component

Author

Listed:
  • Han, Ningning
  • Song, Yumeng
  • Song, Zhanjie

Abstract

The robust principal component analysis (RPCA) refers to the decomposition of an observed matrix into the low-rank component and the sparse component. Conventional methods model the sparse component as pixel-wisely sparse (e.g., ℓ1-norm for the sparsity). However, in many practical scenarios, elements in the sparse part are not truly independently sparse but distributed with contiguous structures. This is the reason why representative RPCA techniques fail to work well in realistic complex situations. To solve this problem, a Bayesian framework for RPCA with structured sparse component is proposed, where both amplitude and support correlation structure are considered simultaneously in recovering the sparse component. The model learning is based on the variational Bayesian inference, which can potentially be applied to estimate the posteriors of all latent variables. Experimental results demonstrate the proposed methodology is validated on synthetic and real data.

Suggested Citation

  • Han, Ningning & Song, Yumeng & Song, Zhanjie, 2017. "Bayesian robust principal component analysis with structured sparse component," Computational Statistics & Data Analysis, Elsevier, vol. 109(C), pages 144-158.
    • Handle: RePEc:eee:csdana:v:109:y:2017:i:c:p:144-158
    DOI: 10.1016/j.csda.2016.12.005
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016794731630295X
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2016.12.005?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. McGrory, C.A. & Titterington, D.M., 2007. "Variational approximations in Bayesian model selection for finite mixture distributions," Computational Statistics & Data Analysis, Elsevier, vol. 51(11), pages 5352-5367, July.
    2. Giordani, Paolo & Kiers, Henk A.L., 2006. "A comparison of three methods for principal component analysis of fuzzy interval data," Computational Statistics & Data Analysis, Elsevier, vol. 51(1), pages 379-397, November.
    3. Manteiga, Wenceslao Gonzalez & Vieu, Philippe, 2007. "Statistics for Functional Data," Computational Statistics & Data Analysis, Elsevier, vol. 51(10), pages 4788-4792, June.
    4. Serneels, Sven & Verdonck, Tim, 2008. "Principal component analysis for data containing outliers and missing elements," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1712-1727, January.
    Full references (including those not matched with items on IDEAS)

    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. Hajargasht, Gholamreza & Rao, D.S. Prasada, 2019. "Multilateral index number systems for international price comparisons: Properties, existence and uniqueness," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 36-47.
    2. Tomáš Želinský, 2015. "Nekonzistentnosť časových preferencií ľudí z arginalizovaných rómskych komunít [On inconsistency of time preferences of people from the marginalised roma communities]," Politická ekonomie, Prague University of Economics and Business, vol. 2015(2), pages 204-222.
    3. Rachdi, Mustapha & Laksaci, Ali & Demongeot, Jacques & Abdali, Abdel & Madani, Fethi, 2014. "Theoretical and practical aspects of the quadratic error in the local linear estimation of the conditional density for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 73(C), pages 53-68.
    4. Amiri, Aboubacar & Crambes, Christophe & Thiam, Baba, 2014. "Recursive estimation of nonparametric regression with functional covariate," Computational Statistics & Data Analysis, Elsevier, vol. 69(C), pages 154-172.
    5. Llop, P. & Forzani, L. & Fraiman, R., 2011. "On local times, density estimation and supervised classification from functional data," Journal of Multivariate Analysis, Elsevier, vol. 102(1), pages 73-86, January.
    6. Meintanis, Simos G. & Hušková, Marie & Hlávka, Zdeněk, 2022. "Fourier-type tests of mutual independence between functional time series," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    7. Berrendero, J.R. & Justel, A. & Svarc, M., 2011. "Principal components for multivariate functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2619-2634, September.
    8. Pigoli, Davide & Sangalli, Laura M., 2012. "Wavelets in functional data analysis: Estimation of multidimensional curves and their derivatives," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1482-1498.
    9. Frahm, Gabriel & Jaekel, Uwe, 2010. "A generalization of Tyler's M-estimators to the case of incomplete data," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 374-393, February.
    10. Gheriballah, Abdelkader & Laksaci, Ali & Sekkal, Soumeya, 2013. "Nonparametric M-regression for functional ergodic data," Statistics & Probability Letters, Elsevier, vol. 83(3), pages 902-908.
    11. Aneiros, Germán & Cao, Ricardo & Fraiman, Ricardo & Genest, Christian & Vieu, Philippe, 2019. "Recent advances in functional data analysis and high-dimensional statistics," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 3-9.
    12. Laurent Delsol, 2013. "No effect tests in regression on functional variable and some applications to spectrometric studies," Computational Statistics, Springer, vol. 28(4), pages 1775-1811, August.
    13. Boj, Eva & Delicado, Pedro & Fortiana, Josep, 2010. "Distance-based local linear regression for functional predictors," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 429-437, February.
    14. García-Escudero, L.A. & Gordaliza, A. & Mayo-Iscar, A. & San Martín, R., 2010. "Robust clusterwise linear regression through trimming," Computational Statistics & Data Analysis, Elsevier, vol. 54(12), pages 3057-3069, December.
    15. repec:dau:papers:123456789/4648 is not listed on IDEAS
    16. Blanco-Fernández, Angela & Corral, Norberto & González-Rodríguez, Gil, 2011. "Estimation of a flexible simple linear model for interval data based on set arithmetic," Computational Statistics & Data Analysis, Elsevier, vol. 55(9), pages 2568-2578, September.
    17. Mustapha Rachdi & Ali Laksaci & Zoulikha Kaid & Abbassia Benchiha & Fahimah A. Al‐Awadhi, 2021. "k‐Nearest neighbors local linear regression for functional and missing data at random," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(1), pages 42-65, February.
    18. López-Pintado, Sara & Romo, Juan, 2011. "A half-region depth for functional data," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1679-1695, April.
    19. T. Górecki & Ł. Smaga, 2017. "Multivariate analysis of variance for functional data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 44(12), pages 2172-2189, September.
    20. Sanjeena Subedi & Paul McNicholas, 2014. "Variational Bayes approximations for clustering via mixtures of normal inverse Gaussian distributions," 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. 8(2), pages 167-193, June.
    21. Jiang, Qing & Hušková, Marie & Meintanis, Simos G. & Zhu, Lixing, 2019. "Asymptotics, finite-sample comparisons and applications for two-sample tests with functional data," Journal of Multivariate Analysis, Elsevier, vol. 170(C), pages 202-220.

    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:eee:csdana:v:109:y:2017:i:c:p:144-158. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.