Unsupervised spectral feature selection with l1-norm graph

Feature selection, which aims to reduce redundancy or noise in the original feature sets, plays an important role in many applications, such as machine learning, multimedia analysis and data mining. Spectral feature selection, a recently proposed method, makes use of spectral clustering to capture underlying manifold structure and achieves excellent performance. However, existing Spectral feature selections suffer from imposing kinds of constraints and lack of clear manifold structure. To address this problem, we propose a new Unsupervised Spectral Feature Selection with l1-Norm Graph, namely USFS. Different from most state-of-art algorithms, the proposed algorithm performs the spectral clustering and l1-Norm Graph jointly to select discriminative features. The manifold structure of original datasets is first learned by the spectral clustering from unlabeled samples, and then it is used to guide the feature selection procedure. Moreover, l1-Norm Graph is imposed to capture clear manifold structure. We also present an efficient iterative optimize method and theoretical convergence analysis of the proposed algorithm. Extensive experimental results on real-world datasets demonstrate the performance of the proposed algorithm.