RMFRASL: Robust Matrix Factorization with Robust Adaptive Structure Learning for Feature Selection

In this paper, we present a novel unsupervised feature selection method termed robust matrix factorization with robust adaptive structure learning (RMFRASL), which can select discriminative features from a large amount of multimedia data to improve the performance of classification and clustering tasks. RMFRASL integrates three models (robust matrix factorization, adaptive structure learning, and structure regularization) into a unified framework. More specifically, a robust matrix factorization-based feature selection (RMFFS) model is proposed by introducing an indicator matrix to measure the importance of features, and the L21-norm is adopted as a metric to enhance the robustness of feature selection. Furthermore, a robust adaptive structure learning (RASL) model based on the self-representation capability of the samples is designed to discover the geometric structure relationships of original data. Lastly, a structure regularization (SR) term is designed on the learned graph structure, which constrains the selected features to preserve the structure information in the selected feature space. To solve the objective function of our proposed RMFRASL, an iterative optimization algorithm is proposed. By comparing our method with some state-of-the-art unsupervised feature selection approaches on several publicly available databases, the advantage of the proposed RMFRASL is demonstrated.