Dimensionality reduction is a challenging task for high-dimensional data processing in machine learning and data mining. It can help to reduce computation time, save storage space and improve the performance of learning algorithms. As an effective dimension reduction technique, unsupervised feature selection aims at finding a subset of features to retain the most relevant information. In this paper, we propose a novel unsupervised feature selection method, called Robust Unsupervised Feature Selection via Matrix Factorization (RUFSM), in which robust discriminative feature selection and robust clustering are performed simultaneously under l(2),(1)-norm while the local manifold structures of data are preserved. The advantages of this work are three-fold. Firstly, both the latent orthogonal cluster centers and the sparse representation of the projected data points based on matrix factorization are predicted for selecting robust discriminative features. Secondly, the feature selection and the clustering are performed simultaneously to guarantee an overall optimum. Thirdly, an efficient iterative update algorithm, which is based on Alternating Direction Method of Multipliers (ADMM), is used for RUFSM optimization. Compared with several state-of-the-art unsupervised feature selection methods, the proposed algorithm comes with better clustering performance for almost all datasets we have experimented with here. (C) 2017 Elsevier B.V. All rights reserved.