Multi-view clustering is an important and fundamental problem. Many multi-view subspace clustering methods have been proposed and achieved success in real-world applications, most of which assume that all views share a same coefficient matrix. However, the underlying information of multiview data are not exploited effectively under this assumption, since the coefficient matrices of different views should have the same clustering properties rather than be the same among multiple views. To this end, a novel Constrained Bilinear Factorization Multi-view Subspace Clustering (CBF-MSC) method is proposed in this paper. Specifically, the bilinear factorization with an orthonormality constraint and a low-rank constraint is employed for all coefficient matrices to make all coefficient matrices have the same trace-norm instead of being equivalent, so as to explore the consensus information of multi-view data more effectively. Finally, an algorithm based on the Augmented Lagrangian Multiplier (ALM) scheme with alternating direction minimization is designed to optimize the objective function. Comprehensive experiments tested on six benchmark datasets validate the effectiveness and competitiveness of the proposed approach compared with several state-of-the-art approaches.
 Data with multiple representations (views) arise naturally in many applications and multi-view algorithms can substantially improve the classification and clustering results. In this work, we study the problem of multi-view clustering and propose a multi-view convex mixture model that locates exemplars (cluster representatives) in the dataset by simultaneously considering all views. Convex mixture models are simplified mixture models that exhibit several attractive characteristics. The proposed algorithm extends the single view convex mixture models so as to handle data with any number of representations, taking into account the diversity of the views while preserving their good properties. Empirical evaluations on synthetic and real data demonstrate the effectiveness and potential of our method. With advances in information acquisition technologies, multi-view data become ubiquitous. Multi-view learning has thus become more and more popular in machine learning and data mining fields. Multi-view unsupervised or semi-supervised learning, such as co-training, co-regularization has gained considerable attention. Although recently, multi-view clustering (MVC) methods have been developed rapidly, there has not been a survey to summarize and analyze the current progress. Therefore, this paper reviews the common strategies for combining multiple views of data and based on this summary we propose a novel taxonomy of the MVC approaches. We further discuss the relationships between MVC and multi-view representation, ensemble clustering, multi-task clustering, multi-view supervised and semi-supervised learning. Several representative real-world applications are elaborated. To promote future development of MVC, we envision several open problems that may require further investigation and thorough examination.