Nonnegative self-representation with a fixed rank constraint for subspace clustering

Abstract A number of approaches to graph-based 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 self-representation with a fixed rank constraint (NSFRC), in which the nonnegative self-representation 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 real-world benchmark datasets demonstrate the superior performance of the proposed method over some state-of-the-art approaches.