Feature Selection and Cancer Classification via Sparse Logistic Regression with the Hybrid L(1/2 +2) Regularization

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 L(1/2 +2) regularization (HLR) function, a linear combination of L(1/2) and L(2) penalties, to select the relevant gene in the logistic regression. The HLR approach inherits some fascinating characteristics from L(1/2) (sparsity) and L(2) (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.