Subspace Clustering by Exploiting a Low-Rank Representation with a Symmetric Constraint

In this paper, we propose a low-rank representation with sym metric constraint (LRRSC) method for robust subspace clust ering. Given a collection of data points approximately drawn from m ultiple subspaces, the proposed technique can simultaneou sly recover the dimension and members of each subspace. LRRSC extends th original low-rank representation algorithm by integrati ng a symmetric constraint into the low-rankness property of high-d imensional data representation. The symmetric low-rank re presentation, which preserves the subspace structures of high-dimension al data, guarantees weight consistency for each pair of data points so that highly correlated data points of subspaces are represented tog ther. Moreover, it can be e fficiently calculated by solving a convex optimization problem. We provide a rigorous proof for minim izing the nuclear-norm regularized least square problem wi th a symmetric constraint. The a ffinity matrix for spectral clustering can be obtained by furth e exploiting the angular information of the principal directions of the symmetric low-rank representa tion. This is a critical step towards evaluating the members hips between data points. Experimental results on benchmark databases d emonstrate the e ffectiveness and robustness of LRRSC compared with several state-of-the-art subspace clustering algorithms .