Abstract:

Logistic regression has been proved as a promising method for machine learning, which focuses on the problem of classification. In this paper, we present an  1₁-1₂-regularized logistic regression model, where the 1₁-norm is responsible for yielding a sparse logistic regression classifier and the  1₂-norm for keeping better classification accuracy. To solve the 1₁1₂-regularized logistic regression model, we develop an alternating direction method of multipliers with embedding limited-Broyden-Fletcher Goldfarb-Shanno (L-BFGS) method. Furthermore, we implement our model for binary classification problems by using real data examples selected from the University of California, Irvine Machines Learning Repository (UCI Repository).We compare our numerical results with those obtained by the well-known LIBSVM and SVM-Light software. The numerical results showthat our 1₁-1₂-regularized logistic regression model achieves better classification and less CPU Time.

Key words: Classification problems , Logistic regression model , Sparsity , Alternating direction method of multipliers