IDEAS home Printed from https://ideas.repec.org/a/spr/stpapr/v64y2023i1d10.1007_s00362-022-01313-z.html
   My bibliography  Save this article

Group linear algorithm with sparse principal decomposition: a variable selection and clustering method for generalized linear models

Author

Listed:
  • Juan C. Laria

    (TomTom Maps-Analytics)

  • M. Carmen Aguilera-Morillo

    (Universitat Politècnica de València
    UC3M-BS Santander Big Data Institute)

  • Rosa E. Lillo

    (UC3M-BS Santander Big Data Institute
    University Carlos III of Madrid)

Abstract

This paper introduces the Group Linear Algorithm with Sparse Principal decomposition, an algorithm for supervised variable selection and clustering. Our approach extends the Sparse Group Lasso regularization to calculate clusters as part of the model fit. Therefore, unlike Sparse Group Lasso, our idea does not require prior specification of clusters between variables. To determine the clusters, we solve a particular case of sparse Singular Value Decomposition, with a regularization term that follows naturally from the Group Lasso penalty. Moreover, this paper proposes a unified implementation to deal with, but not limited to, linear regression, logistic regression, and proportional hazards models with right-censoring. Our methodology is evaluated using both biological and simulated data, and details of the implementation in R and hyperparameter search are discussed.

Suggested Citation

  • Juan C. Laria & M. Carmen Aguilera-Morillo & Rosa E. Lillo, 2023. "Group linear algorithm with sparse principal decomposition: a variable selection and clustering method for generalized linear models," Statistical Papers, Springer, vol. 64(1), pages 227-253, February.
    • Handle: RePEc:spr:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01313-z
    DOI: 10.1007/s00362-022-01313-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00362-022-01313-z
    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/s00362-022-01313-z?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. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    2. Ash A. Alizadeh & Michael B. Eisen & R. Eric Davis & Chi Ma & Izidore S. Lossos & Andreas Rosenwald & Jennifer C. Boldrick & Hajeer Sabet & Truc Tran & Xin Yu & John I. Powell & Liming Yang & Gerald E, 2000. "Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling," Nature, Nature, vol. 403(6769), pages 503-511, February.
    3. Chen, Kun & Chen, Kehui & Müller, Hans-Georg & Wang, Jane-Ling, 2011. "Stringing High-Dimensional Data for Functional Analysis," Journal of the American Statistical Association, American Statistical Association, vol. 106(493), pages 275-284.
    4. Bair, Eric & Hastie, Trevor & Paul, Debashis & Tibshirani, Robert, 2006. "Prediction by Supervised Principal Components," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 119-137, March.
    5. 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.
    6. 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.
    7. Shan Luo & Zehua Chen, 2020. "Feature Selection by Canonical Correlation Search in High-Dimensional Multiresponse Models With Complex Group Structures," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 115(531), pages 1227-1235, July.
    8. 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.
    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. van Wieringen, Wessel N. & Kun, David & Hampel, Regina & Boulesteix, Anne-Laure, 2009. "Survival prediction using gene expression data: A review and comparison," Computational Statistics & Data Analysis, Elsevier, vol. 53(5), pages 1590-1603, March.
    2. Thomas Despois & Catherine Doz, 2022. "Identifying and interpreting the factors in factor models via sparsity : Different approaches," Working Papers halshs-03626503, HAL.
    3. Thomas Despois & Catherine Doz, 2023. "Identifying and interpreting the factors in factor models via sparsity: Different approaches," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 38(4), pages 533-555, June.
    4. Wang Zhu & Wang C.Y., 2010. "Buckley-James Boosting for Survival Analysis with High-Dimensional Biomarker Data," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 9(1), pages 1-33, June.
    5. Caroline Jardet & Baptiste Meunier, 2022. "Nowcasting world GDP growth with high‐frequency data," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 41(6), pages 1181-1200, September.
    6. 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.
    7. 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.
    8. 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.
    9. Mirshani, Ardalan & Reimherr, Matthew, 2021. "Adaptive function-on-scalar regression with a smoothing elastic net," Journal of Multivariate Analysis, Elsevier, vol. 185(C).
    10. Luis A. Barboza & Julien Emile-Geay & Bo Li & Wan He, 2019. "Efficient Reconstructions of Common Era Climate via Integrated Nested Laplace Approximations," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 24(3), pages 535-554, September.
    11. Zemin Zheng & Jinchi Lv & Wei Lin, 2021. "Nonsparse Learning with Latent Variables," Operations Research, INFORMS, vol. 69(1), pages 346-359, January.
    12. Hyun Hak Kim, 2013. "Forecasting Macroeconomic Variables Using Data Dimension Reduction Methods: The Case of Korea," Working Papers 2013-26, Economic Research Institute, Bank of Korea.
    13. Bai, Jushan & Ng, Serena, 2008. "Forecasting economic time series using targeted predictors," Journal of Econometrics, Elsevier, vol. 146(2), pages 304-317, October.
    14. Amir Beck & Yakov Vaisbourd, 2016. "The Sparse Principal Component Analysis Problem: Optimality Conditions and Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 170(1), pages 119-143, July.
    15. Nerea González-García & Ana Belén Nieto-Librero & Purificación Galindo-Villardón, 2023. "CenetBiplot: a new proposal of sparse and orthogonal biplots methods by means of elastic net CSVD," 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. 17(1), pages 5-19, March.
    16. Harold A. Hernández-Roig & M. Carmen Aguilera-Morillo & Rosa E. Lillo, 2021. "Functional Modeling of High-Dimensional Data: A Manifold Learning Approach," Mathematics, MDPI, vol. 9(4), pages 1-22, February.
    17. Lore Zumeta-Olaskoaga & Maximilian Weigert & Jon Larruskain & Eder Bikandi & Igor Setuain & Josean Lekue & Helmut Küchenhoff & Dae-Jin Lee, 2023. "Prediction of sports injuries in football: a recurrent time-to-event approach using regularized Cox models," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(1), pages 101-126, March.
    18. 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.
    19. Davood Hajinezhad & Qingjiang Shi, 2018. "Alternating direction method of multipliers for a class of nonconvex bilinear optimization: convergence analysis and applications," Journal of Global Optimization, Springer, vol. 70(1), pages 261-288, January.
    20. Rosember Guerra-Urzola & Katrijn Van Deun & Juan C. Vera & Klaas Sijtsma, 2021. "A Guide for Sparse PCA: Model Comparison and Applications," Psychometrika, Springer;The Psychometric Society, vol. 86(4), pages 893-919, 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:stpapr:v:64:y:2023:i:1:d:10.1007_s00362-022-01313-z. 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.