Weighted L1-norm logistic regression for gene selection of microarray gene expression classification

The classification of cancer is a significant application of the DNA microarray data. Gene selection methods are ordinarily used handle the issue of high-dimensionality of microarray data to enable experts to diagnose and classify cancer with high accuracy. The penalized logistic regression (PLR) technique is usually used in the dimensionality reduction of the high-dimensional gene expression data sets to remove irrelevant and redundant predictors from the binary logistic regression model. One of the regularization techniques used to achieve this goal is the least absolute shrinkage and selection operator (Lasso). However, this technique has been criticized for being biased in the selection of genes. The adaptive Lasso was usually proposed by assigning an initial weight to each gene to address the selection bias. This paper is concerned with adapting PLR to improve its capability in classification and gene selection, in the sense of accuracy, by introducing the one-dimensional weighted Mahalanobis distance (1-DWM) for each gene as an initial weight inside L₁-norm. By experiments, this proposed method, denoted by adaptive penalized logistic regression (APLR), gives more accurate results compared with other famous methods in this regard. The proposed method is applied to some real high-dimensional gene expression data sets in order to demonstrate its efficiency in terms of classification accuracy and selection of gene. Therefore, the proposed method could be utilized in other studies implementing gene selection in the area of classification of high dimensional cancer data sets.