Unsupervised Maximum Margin Feature Selection with manifold regularization

Feature selection plays a fundamental role in many pattern recognition problems. However, most efforts have been focused on the supervised scenario, while unsupervised feature selection remains as a rarely touched research topic. In this paper, we propose manifold-based maximum margin feature selection (M3FS) to select the most discriminative features for clustering. M3FS targets to find those features that would result in the maximal separation of different clusters and incorporates manifold information by enforcing smoothness constraint on the clustering function. Specifically, we define scale factor for each feature to measure its relevance to clustering, and irrelevant features are identified by assigning zero weights. Feature selection is then achieved by the sparsity constraints on scale factors. Computationally, M3FS is formulated as an integer programming problem and we propose a cutting plane algorithm to efficiently solve it. Experimental results on both toy and real-world data sets demonstrate its effectiveness.