Abstract A Logistic L1/2 regularization model with its efficient solution algorithm is proposed. By the proposed model, which is constructed on the basis of the L1/2 regularization theory, the variable selection capability is enhanced and the over-fitting problem of the traditional model is alleviated. The proposed algorithm with high computational efficiency is designed by the coordinate descent technique. The experimental results on synthetic and real datasets indicate that the proposed method outperforms the traditional Logistic regression and the L1 regularized Logistic regression on both variable selection and tendency prediction.
[1] Ayalew L,Yamagishi H.The Application of GIS-Based Logistic Regression for Landslide Susceptibility Mapping in the Kakuda-Yahiko Mountains,Central Japan.Geomorphology,2005,65(1/2): 15-31 [2] Azzalini A.Logistic Regression for Autocorrelated Data with Application to Repeated Measures.Biometrika,1994,81(4): 767-775 [3] King G,Zeng L.Logistic Regression in Rare Events Data.Political Analysis,2001,9(2): 137-163 [4] Valenzuela T,Roe D,Cretin S,et al.Estimating Effectiveness of Cardiac Arrest Interventions: A Logistic Regression Survival Model.Circulation,1997,96(10): 3308-3313 [5] Keating K,Cherry S.Use and Interpretation of Logistic Regression in Habitat-Selection Studies.Journal of Wildlife Management,2004,68(4): 774-789 [6] McCullagh P,Nelder J.Generalized Linear Models.New York,USA: Chapman and Hall,1999 [7] Zhu Ji,Hastie T.Classification of Gene Microarrays by Penalized Logistic Regression.Biostatistics,2004,5(2): 427-443 [8] Park M,Hastie T.L1-Regularization Path Algorithm for Generalized Linear Models.Journal of Royal Statistical Society: Series B,2007,69(4): 659-677 [9] Genkin A,Lewis D,Madigan D.Large-Scale Bayesian Logistic Regression for Text Categorization.Technometrics,2007,49(3): 291-304 [10] Koh K,Kim S,Boyd S.An Interior-Point Method for Large-Scale L1-Regularized Logistic Regression.Journal of Machine Learning Research,2007,8: 1519-1555 [11] Yuan Guoxun,Ho C H,Lin C J,An Improved GLMNET for L1-Regularized Logistic Regression // Proc of the 17th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining.San Diego,USA,2011: 33-41 [12] Xu Zongben,Zhang Hai,Wang Yao,et al.L1/2 Regularization.Science China: Information Sciences,2010,53(6): 1159-1169 [13] Xu Zongben,Chang Xiangyu,Xu Fengmin,et al.L1/2 Regularization: A Thresholding Representation Theory and a Fast Solver.IEEE Trans on Neural Networks and Learning Systems,2012,23(7): 1013-1027 [14] Xu Zongben,Guo Hailiang,Wang Yao,et al.The Representative of L1/2 Regularization among Lq (0<q≤1) Regularizations: An Experimental Study Based on Phase Diagram.Acta Automatica Sinica,2012,38(7): 1225-1228 (in Chinese) (徐宗本,郭海亮,王 尧,等.L1/2 正则子在Lq (0<q≤1)正则子中的代表性:基于相位图的实验研究.自动化学报,2012,38(7): 1225-1228) [15] Friedman J,Hastie T,Tibshirani R.Regularization Paths for Generalized Linear Models via Coordinate Descent.Journal of Statistical Software,2010,33(1): 1-22 [16] Tibshirani R.Regression Shrinkage and Selection via the Lasso.Journal of Royal Statistical Society: Series B,1996,58(1): 229-243 [17] Donoho D.Compressed Sensing.IEEE Trans on Information Theory,2006,52(4): 1289-1306 [18] Wright J,Yang A,Ganesh A,et al.Robust Face Recognition via Sparse Representation.IEEE Trans on Pattern Analysis and Machine Intelligence,2008,31(2): 210-227 [19] Xing Fuchong.Investigation on Solutions of Cubic Equations with One Unknown.Journal of The Central University for Nationalities: Natural Science Edition,2003,12(3): 207-218 (in Chinese) (邢富冲.一元三次方程求解新探.中央民族大学学报:自然科学版,2003,12(3): 207-218) [20] Alon U,Barkai N,Notterman D,et al.Broad Patterns of Gene Expression Revealed by Clustering Analysis of Tumor and Normal Colon Cancer Tissues.Cell Biology,1999,96(12): 6745-6750
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