IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v15y2021i3d10.1007_s11634-020-00435-2.html
   My bibliography  Save this article

Sparse principal component regression via singular value decomposition approach

Author

Listed:
  • Shuichi Kawano

    (The University of Electro-Communications)

Abstract

Principal component regression (PCR) is a two-stage procedure: the first stage performs principal component analysis (PCA) and the second stage builds a regression model whose explanatory variables are the principal components obtained in the first stage. Since PCA is performed using only explanatory variables, the principal components have no information about the response variable. To address this problem, we present a one-stage procedure for PCR based on a singular value decomposition approach. Our approach is based upon two loss functions, which are a regression loss and a PCA loss from the singular value decomposition, with sparse regularization. The proposed method enables us to obtain principal component loadings that include information about both explanatory variables and a response variable. An estimation algorithm is developed by using the alternating direction method of multipliers. We conduct numerical studies to show the effectiveness of the proposed method.

Suggested Citation

  • Shuichi Kawano, 2021. "Sparse principal component regression via singular value decomposition approach," 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. 15(3), pages 795-823, September.
    • Handle: RePEc:spr:advdac:v:15:y:2021:i:3:d:10.1007_s11634-020-00435-2
    DOI: 10.1007/s11634-020-00435-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11634-020-00435-2
    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/s11634-020-00435-2?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. Zou, Hui, 2006. "The Adaptive Lasso and Its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 1418-1429, December.
    2. Kawano, Shuichi & Fujisawa, Hironori & Takada, Toyoyuki & Shiroishi, Toshihiko, 2015. "Sparse principal component regression with adaptive loading," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 192-203.
    3. Shen, Haipeng & Huang, Jianhua Z., 2008. "Sparse principal component analysis via regularized low rank matrix approximation," Journal of Multivariate Analysis, Elsevier, vol. 99(6), pages 1015-1034, July.
    4. Xinfeng Chang & Hu Yang, 2012. "Combining two-parameter and principal component regression estimators," Statistical Papers, Springer, vol. 53(3), pages 549-562, August.
    5. Ye, Gui-Bo & Xie, Xiaohui, 2011. "Split Bregman method for large scale fused Lasso," Computational Statistics & Data Analysis, Elsevier, vol. 55(4), pages 1552-1569, April.
    6. Li, Baibing & Martin, Elaine B. & Morris, A. Julian, 2002. "On principal component analysis in L1," Computational Statistics & Data Analysis, Elsevier, vol. 40(3), pages 471-474, September.
    7. Ian T. Jolliffe, 1982. "A Note on the Use of Principal Components in Regression," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 31(3), pages 300-303, November.
    8. Fan J. & Li R., 2001. "Variable Selection via Nonconcave Penalized Likelihood and its Oracle Properties," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1348-1360, December.
    9. Robert Jennrich, 2006. "Rotation to Simple Loadings Using Component Loss Functions: The Oblique Case," Psychometrika, Springer;The Psychometric Society, vol. 71(1), pages 173-191, March.
    10. Hyonho Chun & Sündüz Keleş, 2010. "Sparse partial least squares regression for simultaneous dimension reduction and variable selection," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 3-25, January.
    11. Patrick Danaher & Pei Wang & Daniela M. Witten, 2014. "The joint graphical lasso for inverse covariance estimation across multiple classes," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 76(2), pages 373-397, March.
    12. Reiss, Philip T. & Ogden, R. Todd, 2007. "Functional Principal Component Regression and Functional Partial Least Squares," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 984-996, September.
    13. Kawano, Shuichi & Fujisawa, Hironori & Takada, Toyoyuki & Shiroishi, Toshihiko, 2018. "Sparse principal component regression for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 180-196.
    14. 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.
    15. Manuel Febrero-Bande & Pedro Galeano & Wenceslao González-Manteiga, 2017. "Functional Principal Component Regression and Functional Partial Least-squares Regression: An Overview and a Comparative Study," International Statistical Review, International Statistical Institute, vol. 85(1), pages 61-83, April.
    16. 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.
    17. Shujie Ma & Jian Huang, 2017. "A Concave Pairwise Fusion Approach to Subgroup Analysis," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(517), pages 410-423, January.
    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. Emmanuel Jordy Menvouta & Sven Serneels & Tim Verdonck, 2022. "Sparse dimension reduction based on energy and ball statistics," 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. 16(4), pages 951-975, December.

    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. Kawano, Shuichi & Fujisawa, Hironori & Takada, Toyoyuki & Shiroishi, Toshihiko, 2018. "Sparse principal component regression for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 124(C), pages 180-196.
    2. Kawano, Shuichi & Fujisawa, Hironori & Takada, Toyoyuki & Shiroishi, Toshihiko, 2015. "Sparse principal component regression with adaptive loading," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 192-203.
    3. Mihee Lee & Haipeng Shen & Jianhua Z. Huang & J. S. Marron, 2010. "Biclustering via Sparse Singular Value Decomposition," Biometrics, The International Biometric Society, vol. 66(4), pages 1087-1095, December.
    4. Iason Kynigakis & Ekaterini Panopoulou, 2022. "Does model complexity add value to asset allocation? Evidence from machine learning forecasting models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 37(3), pages 603-639, April.
    5. Yan Li & Chun Yu & Yize Zhao & Weixin Yao & Robert H. Aseltine & Kun Chen, 2022. "Pursuing sources of heterogeneity in modeling clustered population," Biometrics, The International Biometric Society, vol. 78(2), pages 716-729, June.
    6. Tanin Sirimongkolkasem & Reza Drikvandi, 2019. "On Regularisation Methods for Analysis of High Dimensional Data," Annals of Data Science, Springer, vol. 6(4), pages 737-763, December.
    7. Luo, Ruiyan & Qi, Xin, 2015. "Sparse wavelet regression with multiple predictive curves," Journal of Multivariate Analysis, Elsevier, vol. 134(C), pages 33-49.
    8. Kei Hirose & Miyuki Imada, 2018. "Sparse factor regression via penalized maximum likelihood estimation," Statistical Papers, Springer, vol. 59(2), pages 633-662, June.
    9. Tutz, Gerhard & Pößnecker, Wolfgang & Uhlmann, Lorenz, 2015. "Variable selection in general multinomial logit models," Computational Statistics & Data Analysis, Elsevier, vol. 82(C), pages 207-222.
    10. Margherita Giuzio, 2017. "Genetic algorithm versus classical methods in sparse index tracking," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 40(1), pages 243-256, November.
    11. Yize Zhao & Matthias Chung & Brent A. Johnson & Carlos S. Moreno & Qi Long, 2016. "Hierarchical Feature Selection Incorporating Known and Novel Biological Information: Identifying Genomic Features Related to Prostate Cancer Recurrence," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1427-1439, October.
    12. Gareth M. James & Peter Radchenko & Jinchi Lv, 2009. "DASSO: connections between the Dantzig selector and lasso," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 127-142, January.
    13. Umberto Amato & Anestis Antoniadis & Italia De Feis & Irene Gijbels, 2021. "Penalised robust estimators for sparse and high-dimensional linear models," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 30(1), pages 1-48, March.
    14. Camila Epprecht & Dominique Guegan & Álvaro Veiga & Joel Correa da Rosa, 2017. "Variable selection and forecasting via automated methods for linear models: LASSO/adaLASSO and Autometrics," Post-Print halshs-00917797, HAL.
    15. Wang, Christina Dan & Chen, Zhao & Lian, Yimin & Chen, Min, 2022. "Asset selection based on high frequency Sharpe ratio," Journal of Econometrics, Elsevier, vol. 227(1), pages 168-188.
    16. Peter Bühlmann & Jacopo Mandozzi, 2014. "High-dimensional variable screening and bias in subsequent inference, with an empirical comparison," Computational Statistics, Springer, vol. 29(3), pages 407-430, June.
    17. Peter Martey Addo & Dominique Guegan & Bertrand Hassani, 2018. "Credit Risk Analysis Using Machine and Deep Learning Models," Risks, MDPI, vol. 6(2), pages 1-20, April.
    18. Capanu, Marinela & Giurcanu, Mihai & Begg, Colin B. & Gönen, Mithat, 2023. "Subsampling based variable selection for generalized linear models," Computational Statistics & Data Analysis, Elsevier, vol. 184(C).
    19. Weng, Jiaying, 2022. "Fourier transform sparse inverse regression estimators for sufficient variable selection," Computational Statistics & Data Analysis, Elsevier, vol. 168(C).
    20. Ander Wilson & Brian J. Reich, 2014. "Confounder selection via penalized credible regions," Biometrics, The International Biometric Society, vol. 70(4), pages 852-861, December.

    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:advdac:v:15:y:2021:i:3:d:10.1007_s11634-020-00435-2. 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.