Top-k Feature Selection Framework Using Robust 0-1 Integer Programming.

Feature selection (FS), which identifies the relevant features in a data set to facilitate subsequent data analysis, is a fundamental problem in machine learning and has been widely studied in recent years. Most FS methods rank the features in order of their scores based on a specific criterion and then select the k top-ranked features, where k is the number of desired features. However, these features are usually not the top- k features and may present a suboptimal choice. To address this issue, we propose a novel FS framework in this article to select the exact top- k features in the unsupervised, semisupervised, and supervised scenarios. The new framework utilizes the l0,2 -norm as the matrix sparsity constraint rather than its relaxations, such as the l1,2 -norm. Since the l0,2 -norm constrained problem is difficult to solve, we transform the discrete l0,2 -norm-based constraint into an equivalent 0-1 integer constraint and replace the 0-1 integer constraint with two continuous constraints. The obtained top- k FS framework with two continuous constraints is theoretically equivalent to the l0,2 -norm constrained problem and can be optimized by the alternating direction method of multipliers (ADMM). Unsupervised and semisupervised FS methods are developed based on the proposed framework, and extensive experiments on real-world data sets are conducted to demonstrate the effectiveness of the proposed FS framework.