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

Author

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Eddelbuettel, Dirk & Francois, Romain, 2011. "Rcpp: Seamless R and C++ Integration," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 40(i08).
    Full references (including those not matched with items on IDEAS)

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