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Nonnegative matrix factorization (NMF) and spectral clustering are two of the most widely used clustering techniques. However, NMF cannot deal with the nonlinear data, and spectral clustering relies on the postprocessing. In this article, we propose a Robust Matrix factorization with Spectral embedding (RMS) approach for data clustering, which inherits the advantages of NMF and spectral clustering, while avoiding their shortcomings. In addition, to cluster the data represented by multiple views, we present the multiview version of RMS (M-RMS), and the weights of different views are self-tuned. The main contributions of this research are threefold: 1) by integrating spectral clustering and matrix factorization, the proposed methods are able to capture the nonlinear data structure and obtain the cluster indicator directly; 2) instead of using the squared Frobenius-norm, the objectives are developed with the $\ell _{2,1}$ -norm, such that the effects of the outliers are alleviated; and 3) the proposed methods are totally parameter-free, which increases the applicability for various real-world problems. Extensive experiments on several single-view/multiview data sets demonstrate the effectiveness of our methods and verify their superior clustering performance over the state of the arts. [ABSTRACT FROM AUTHOR]

Linear discriminant analysis (LDA) has been widely used as the technique of feature exaction. However, LDA may be invalid to address the data from different domains. The reasons are as follows: 1) the distribution discrepancy of data may disturb the linear transformation matrix so that it cannot extract the most discriminative feature and 2) the original design of LDA does not consider the unlabeled data so that the unlabeled data cannot take part in the training process for further improving the performance of LDA. To address these problems, in this brief, we propose a novel transferable LDA (TLDA) method to extend LDA into the scenario in which the data have different probability distributions. The whole learning process of TLDA is driven by the philosophy that the data from the same subspace have a low-rank structure. The matrix rank in TLDA is the key learning criterion to conduct local and global linear transformations for restoring the low-rank structure of data from different distributions and enlarging the distances among different subspaces. In doing so, the variations of distribution discrepancy within the same subspace can be reduced, i.e., data can be aligned well and the maximally separated structure can be achieved for the data from different subspaces. A simple projected subgradient-based method is proposed to optimize the objective of TLDA, and a strict theory proof is provided to guarantee a quick convergence. The experimental evaluation on public data sets demonstrates that our TLDA can achieve better classification performance and outperform the state-of-the-art methods. [ABSTRACT FROM AUTHOR]