Dual Graph Regularized Compact Feature Representation for Unsupervised Feature Selection

Abstract As one of the dimensionality reduction methods, unsupervised feature selection aims to select a subset of original features without the labels of data instances. It becomes more and more important since large amounts of unlabelled high dimensional data need to be processed in many machine learning and data mining tasks. In this paper, we propose a novel unsupervised feature selection method via compact feature representation, with the local geometrical structure of data being preserved by using a dual Laplacian graph regularization term. In detail, different to many previous representation based methods which use the original data as representation dictionary, we propose to learn a feature dictionary subspace for compact and robust feature representation. During the dictionary learning process, the l 2, 1 -norm is imposed on the combination coefficient matrix to select discriminate features for constructing the latent feature dictionary. Meanwhile, the local geometrical structure of original data is preserved from the perspectives of subspace learning and feature representation. In general, our method conducts dictionary learning and unsupervised feature selection simultaneously. We develop an efficient optimization algorithm based on Alternating Direction Method of Multipliers to solve the proposed optimization problem and experiments on various types of real world datasets are conducted to demonstrate the effectiveness of the proposed method.