Enhancing low-rank subspace clustering by manifold regularization

Recently, low-rank representation (LRR) method has achieved great success in subspace clustering, which aims to cluster the data points that lie in a union of low-dimensional subspace. Given a set of data points, LRR seeks the lowest rank representation among the many possible linear combinations of the bases in a given dictionary or in terms of the data itself. However, LRR only considers the global Euclidean structure, while the local manifold structure, which is often important for many real applications, is ignored. In this paper, to exploit the local manifold structure of the data, a manifold regularization characterized by a Laplacian graph has been incorporated into LRR, leading to our proposed Laplacian regularized LRR (LapLRR). An efficient optimization procedure, which is based on alternating direction method of multipliers, is developed for LapLRR. Experimental results on synthetic and real data sets are presented to demonstrate that the performance of LRR has been enhanced by using the manifold regularization.