From Joint Feature Selection and Self-Representation Learning to Robust Multi-view Subspace Clustering

In era of big data, we have easier access to the data with multi-view representations from heterogeneous feature spaces, where each view is often unlabeled, partial and even full of noises. These unique challenges and properties motivate us to develop a novel robust multi-view subspace clustering framework (RMSC), which learns a consensus affinity matrix with the ideal subspace structure, by extending our joint feature selection and self-representation model (JFSSR). Concretely, RMSC learns the consensus graph across diverse views with exactly k connected components (k is the number of clusters), which is encoded by a block diagonal self-representation matrix. Besides, we emphasize l2;1-norm minimization on the loss function to reduce redundant and irrelevant features, and implicitly assign an adaptive weight to each view without introducing additional parameters. Lastly, an alternating optimization algorithm is derived to solve the nonconvex formulated objective. Extensive empirical results on both synthetic data and real-world benchmark data sets show that RMSC consistently outperforms several representative multiview clustering approaches.