Unsupervised feature selection via multiple graph fusion and feature weight learning

Unsupervised feature selection attempts to select a small number of discriminative features from original high-dimensional data and preserve the intrinsic data structure without using data labels. As an unsupervised learning task, most previous methods often use a coefficient matrix for feature reconstruction or feature projection, and a certain similarity graph is widely utilized to regularize the intrinsic structure preservation of original data in a new feature space. However, a similarity graph with poor quality could inevitably afect the final results. In addition, designing a rational and efective feature reconstruction/projection model is not easy. In this paper, we introduce a novel and efective unsupervised feature selection method via multiple graph fusion and feature weight learning(MGF2WL) to address these issues. Instead of learning the feature coefficient matrix, we directly learn the weights of diferent feature dimensions by introducing a feature weight matrix, and the weighted features are projected into the label space. Aiming to exploit sufficient relation of data samples, we develop a graph fusion term to fuse multiple predefined similarity graphs for learning a unified similarity graph, which is then deployed to regularize the local data structure of original data in a projected label space. Finally, we design a block coordinate descent algorithm with a convergence guarantee to solve the resulting optimization problem. Extensive experiments with sufficient analyses on various datasets are conducted to validate the efficacy of our proposed MGF2WL.