$\hbox {U}^2\hbox {F}^2\hbox {S}^2$: Uncovering Feature-level Similarities for Unsupervised Feature Selection

Abstract

Unsupervised feature selection is a critical technique in processing high dimensional data containing redundant and noisy features. Based on sample-level similarities, conventional algorithms select features that can preserve the local structure of data points. However, the similarities among all dimensions of features, which play important roles in feature selection, are neglected. In this paper, we propose a novel method dubbed $\hbox {U}^2\hbox {F}^2\hbox {S}^2$ by uncovering these pivotal similarities for unsupervised feature selection. A feature-level similarity uncovering loss function is first presented to preserve the local structure of data points at the feature level. Specially, we propose two schemes to measure the feature-level similarities from different perspectives. Then, a joint framework of feature selection and clustering is developed to capture the underlying cluster information. The objective function is efficiently optimized by our proposed iterative algorithm. Extensive experimental results on six publicly available databases demonstrate that $\hbox {U}^2\hbox {F}^2\hbox {S}^2$ outperforms the state-of-the-arts.