Maximum Block Energy Guided Robust Subspace Clustering

Subspace clustering is useful for clustering data points according to the underlying subspaces. Many methods have been presented in recent years, among which Sparse Subspace Clustering (SSC), Low-Rank Representation (LRR) and Least Squares Regression clustering (LSR) are three representative methods. These approaches achieve good results by assuming the structure of errors as a prior and removing errors in the original input space by modeling them in their objective functions. In this paper, we propose a novel method from an energy perspective to eliminate errors in the projected space rather than the input space. Since the block diagonal property can lead to correct clustering, we measure the correctness in terms of a block in the projected space with an energy function. A correct block corresponds to the subset of columns with the maximal energy. The energy of a block is defined based on the unary column, pairwise and high-order similarity of columns for each block. We relax the energy function of a block and approximate it by a constrained homogenous function. Moreover, we propose an efficient iterative algorithm to remove errors in the projected space. Both theoretical analysis and experiments show the superiority of our method over existing solutions to the clustering problem, especially when noise exists.