Fused Lasso for Feature Selection using Structural Information

Feature selection has been proven a powerful preprocessing step for high-dimensional data analysis. However, most state-of-the-art methods suffer from two major drawbacks. First, they usually overlook the structural correlation information between pairwise samples, which may encapsulate useful information for refining the performance of feature selection. Second, they usually consider candidate feature relevancy equivalent to selected feature relevancy, and some less relevant features may be misinterpreted as salient features. To overcome these issues, we propose a new fused lasso for feature selection using structural information. Our idea is based on converting the original vectorial features into structure-based feature graph representations to incorporate structural relationship between samples, and defining a new evaluation measure to compute the joint significance of pairwise feature combinations in relation to the target feature graph. Furthermore, we formulate the corresponding feature subset selection problem into a least square regression model associated with a fused lasso regularizer to simultaneously maximize the joint relevancy and minimize the redundancy of the selected features. To effectively solve the challenging optimization problem, an iterative algorithm is developed to identify the most discriminative features. Experiments demonstrate the effectiveness of the proposed approach.