The result of the literature.

In bold–the best performance.</p

Feature Selection and Cancer Classification via Sparse Logistic Regression with the Hybrid L_{1/2 +2} Regularization

<div><p>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 L₂ penalties, to select the relevant gene in the logistic regression. The HLR approach inherits some fascinating characteristics from L_1/2 (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.</p></div

Mean results of empirical datasets.

<p>In bold–the best performance.</p

Mean results of the simulation.

<p>In bold–the best performance amongst all the methods.</p

The most frequently selected 10 genes found by the five sparse logistic regression methods from the lung cancer dataset.

<p>The most frequently selected 10 genes found by the five sparse logistic regression methods from the lung cancer dataset.</p

The validation results of the classifiers based on the top rank selected genes from lung cancer dataset.

<p>In bold–the best performance.</p

The performance of the AUC from ROC analyzes of each method on prostate, lymphoma and lung cancer datasets.

<p>The performance of the AUC from ROC analyzes of each method on prostate, lymphoma and lung cancer datasets.</p

Contour plots (two-dimensional) for the regularization methods.

<p>The regularization parameters are <i>λ</i> = 1 and <i>α</i> = 0.2 for the HLR method.</p

Real datasets used in this paper.

<p>Real datasets used in this paper.</p