Nonnegative SelfRepresentation with a Fixed Rank Constraint for Subspace Clustering Abstract   A number of approaches to graphbased subspace clustering, which assumes that the clustered data points were drawn from an unknown union of multiple subspaces, have been proposed in recent years. Despite their successes in computer vision and data mining, most neglect to simultaneously consider global and local information, which may improve clustering performance. On the other hand, the number of connected components reflected by the learned affinity matrix is commonly inconsistent with the true number of clusters. To this end, we propose an adaptive affinity matrix learning method, nonnegative selfrepresentation with a fixed rank constraint (NSFRC), in which the nonnegative selfrepresentation and an adaptive distance regularization jointly uncover the intrinsic structure of data. In particular, a fixed rank constraint as a prior is imposed on the Laplacian matrix associated with the data representation coefficients to urge the true number of clusters to exactly equal the number of connected components in the learned affinity matrix. Also, we derive an efficient iterative algorithm based on an augmented Lagrangian multiplier to optimize NSFRC. Extensive experiments conducted on realworld benchmark datasets demonstrate the superior performance of the proposed method over some stateoftheart approaches.

From Joint Feature Selection and SelfRepresentation Learning to Robust Multiview Subspace Clustering In era of big data, we have easier access to the data with multiview 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 multiview subspace clustering framework (RMSC), which learns a consensus affinity matrix with the ideal subspace structure, by extending our joint feature selection and selfrepresentation 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 selfrepresentation matrix. Besides, we emphasize l2;1norm 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 realworld benchmark data sets show that RMSC consistently outperforms several representative multiview clustering approaches.