Low-rank representation with graph regularization for subspace clustering

In this paper, we propose a low-rank representation method that incorporates graph regularization for robust subspace clustering. We make the assumption that high-dimensional data can be approximated as the union of low-dimensional subspaces of unknown dimension. The proposed method extends the low-rank representation algorithm by incorporating graph regularization with a discriminative dictionary. Existing low-rank representation methods for subspace clustering use noisy data as the dictionary. The proposed technique, however, takes advantage of the discriminative dictionary to seek the lowest-rank representation by virtue of matrix recovery and completion techniques. Moreover, the discriminative dictionary is further used to construct a graph Laplacian to separate the low-rank representation of high-dimensional data. The proposed algorithm can recover the low-dimensional subspace structure from high-dimensional observations (which are often corrupted by gross errors). Simultaneously, the samples are clustered into their corresponding underlying subspaces. Extensive experimental results on benchmark databases demonstrate the efficiency and effectiveness of the proposed algorithm for subspace clustering.