Unsupervised feature selection via Diversity-induced Self-representation

Feature selection is to select a subset of relevant features from the original feature set. In practical applications, regarding the unavailability of an amount of the labels is still a challenging problem. To overcome this problem, unsupervised feature selection algorithms have been developed and achieve promising performance. However, most existing approaches consider only the representativeness of features, but the diversity of features which may lead to the high redundancy and the losses of valuable features are ignored. In this paper, we propose a Diversity-induced Self-representation (DISR) based unsupervised feature selection method to effectively select the features with both representativeness and diversity. Specifically, based on the inherent self-representation property of features, the most representative features can be selected. Meanwhile, to preserve the diversity of selected features and reduce the redundancy of the original features as soon as possible, we introduce a novel diversity term, which adjusts the weights of selected features by incorporating the similarities between features. We then present an efficient algorithm to solve the optimization problem by using the inexact Augmented Lagrange Method (ALM). Finally, both clustering and classification tasks are used to evaluate the proposed method. Empirical results on the synthetic dataset and nine real-world datasets demonstrate the superiority of our method compared with state-of-the-art algorithms.