Subspace Clustering via New Low-Rank Model with Discrete Group Structure Constraint

We propose a new subspace clustering model to segment data which is drawn from multiple linear or affine subspaces. Unlike the well-known sparse subspace clustering (SSC) and low-rank representation (LRR) which transfer the subspace clustering problem into two steps’ algorithm including building the affinity matrix and spectral clustering, our proposed model directly learns the different subspaces’ indicator so that low-rank based different groups are obtained clearly. To better approximate the low-rank constraint, we suggest to use Schatten p-norm to relax the rank constraint instead of using trace norm. We tactically avoid the integer programming problem imposed by group indicator constraint to let our algorithm more efficient and scalable. Furthermore, we extend our discussion to the general case in which subspaces don’t pass the original point. The new algorithm’s convergence is given, and both synthetic and real world datasets demonstrate our proposed model’s effectiveness.