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Feature Selection and Cancer Classification via Sparse Logistic Regression with the Hybrid L1/2 +2 Regularization

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  • Hai-Hui Huang
  • Xiao-Ying Liu
  • Yong Liang

Abstract

Cancer classification and feature (gene) selection plays an important role in knowledge discovery in genomic data. Although logistic regression is one of the most popular classification methods, it does not induce feature selection. In this paper, we presented a new hybrid L1/2 +2 regularization (HLR) function, a linear combination of L1/2 and L2 penalties, to select the relevant gene in the logistic regression. The HLR approach inherits some fascinating characteristics from L1/2 (sparsity) and L2 (grouping effect where highly correlated variables are in or out a model together) penalties. We also proposed a novel univariate HLR thresholding approach to update the estimated coefficients and developed the coordinate descent algorithm for the HLR penalized logistic regression model. The empirical results and simulations indicate that the proposed method is highly competitive amongst several state-of-the-art methods.

Suggested Citation

  • Hai-Hui Huang & Xiao-Ying Liu & Yong Liang, 2016. "Feature Selection and Cancer Classification via Sparse Logistic Regression with the Hybrid L1/2 +2 Regularization," PLOS ONE, Public Library of Science, vol. 11(5), pages 1-15, May.
    • Handle: RePEc:plo:pone00:0149675
    DOI: 10.1371/journal.pone.0149675
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    References listed on IDEAS

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    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. 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.
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    Cited by:

    1. Zakariya Yahya Algamal & Muhammad Hisyam Lee, 2019. "A two-stage sparse logistic regression for optimal gene selection in high-dimensional microarray data classification," 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. 13(3), pages 753-771, September.
    2. Xia Zheng & Yaohua Rong & Ling Liu & Weihu Cheng, 2021. "A More Accurate Estimation of Semiparametric Logistic Regression," Mathematics, MDPI, vol. 9(19), pages 1-12, September.
    3. Sai Wang & Hai-Wei Shen & Hua Chai & Yong Liang, 2019. "Complex harmonic regularization with differential evolution in a memetic framework for biomarker selection," PLOS ONE, Public Library of Science, vol. 14(2), pages 1-21, February.
    4. Sangjin Kim & Jong-Min Kim, 2019. "Two-Stage Classification with SIS Using a New Filter Ranking Method in High Throughput Data," Mathematics, MDPI, vol. 7(6), pages 1-16, May.
    5. Thilde Terkelsen & Anders Krogh & Elena Papaleo, 2020. "CAncer bioMarker Prediction Pipeline (CAMPP)—A standardized framework for the analysis of quantitative biological data," PLOS Computational Biology, Public Library of Science, vol. 16(3), pages 1-20, March.
    6. Lizhen Shen & Hua Jiang & Mingfang He & Guoqing Liu, 2017. "Collaborative representation-based classification of microarray gene expression data," PLOS ONE, Public Library of Science, vol. 12(12), pages 1-14, December.

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