Regularized NonNegative Spectral Embedding for Clustering Spectral Clustering is a popular technique to split data points into groups, especially for complex datasets. The algorithms in the Spectral Clustering family typically consist of multiple separate stages (such as similarity matrix construction, lowdimensional embedding, and KMeans clustering as postprocessing), which may lead to suboptimal results because of the possible mismatch between different stages. In this paper, we propose an endtoend singlestage learning method to clustering called Regularized Nonnegative Spectral Embedding (RNSE) which extends Spectral Clustering with the adaptive learning of similarity matrix and meanwhile utilizes nonnegative constraints to facilitate onestep clustering (directly from data points to clustering labels). Two wellfounded methods, successive alternating projection and strategic multiplicative update, are employed to work out the quite challenging optimization problems in RNSE. Extensive experiments on both synthetic and realworld datasets demonstrate RNSEu0027s superior clustering performance to some stateoftheart competitors.

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.