Novel regularization method for biomarker selection and cancer classification

Variable selection has attracted more attention in big data and machine learning fields. In high dimensional data analysis, many relevant variables or variable groups are widely found. For example, people pay more interests to biological pathway or regulatory network in microarray gene expression data. In recent years, regularization methods are commonly used approaches for variable selection. Existing regularization methods generally use $L_2$ L 2 penalty to evaluate the grouping effect and $L_q~(0 L q ( 0 q 1 ) penalty with a fixed value of $q$ q to evaluate the variable sparsity, respectively. These methods typically produce a good performance with high efficiency, but they often require the data to satisfy a certain probability distribution. In this paper, we propose a novel complex harmonic regularization (CHR) penalty function, which can approximate the combination of $L_q~(\frac{1}{2} \leq q \leq 1)$ L q ( 1 2 ≤ q ≤ 1 ) and $L_p~(1 L p ( 1 p 2 ) regularizations with adjustable $p$ p and $q$ q to select the groups of the relevant variables. The CHR penalty function can be effectively solved by a direct path seeking algorithm. We demonstrate that the proposed CHR penalty function performs better than the state-of-the-art regularization methods in selecting groups of relevant variables and classification.