Sparse subspace clustering with low-rank transformation

In order to solve the problem that sparse subspace clustering cannot effectively cluster the dataset under non-independent assumption, this paper proposes the sparse subspace clustering with low-rank transformation, which merges the low-rank transformation into sparse subspace clustering. The low-rank transformation can not only reduce variations within the subspaces, but also increase separations between the subspaces. This guarantees that property of these datasets is altered from inconsistent independent assumption to asymptotic consistent independent assumption, ultimately to consistent independent assumption. Sparse subspace clustering with low-rank transformation is formulated as the minimization optimizations with two variables, which can be solved by an iterative strategy including the clustering and computing the optimal transformation. Experimental results on the synthetic datasets show that sparse subspace clustering with low-rank transformation is robust to synthetic dataset with noise and its classification error is approximately 75% lower than that of sparse subspace clustering. Experimental results on face clustering on the Yale Extend B dataset and motion segmentation on Hopkins 155 dataset show that the proposed approach significantly outperforms sparse subspace clustering.