Correlation Self-Expression Shrunk for Subspace Clustering

In subspace clustering, low-rank representation (LRR) is a nice recipe for learning a good affinity matrix of a set of unlabeled data by representing themselves under the low-rank constraint in order to subsequently couple with clustering methods to divide data into several groups. However, the underlying geometric structure within data is still insufficiently explored in LRR. For this reason, we propose a correlation self-expression shrunk (CSS) to refresh LRR with two novel insights: 1) the compound schatten p -norm instead of the nuclear norm which is used to induce adaptive affinity matrix by addressing the issues of both sparse and dense representation; 2) to model compact group structure and relieve side effect of the outliers, CSS designs a robust self-expression shrunk regularization to reduce the deviation of similar samples. Thus, CSS can reap the benefits of both insights to boost clustering performance. In addition, we optimize CSS in the frame of alternating direction multiplier method (ADMM) where each sub-problem has a closed-form solution. Experiments of image clustering on four datasets verify the efficacy of CSS against several baseline variants of LRR.