A Novel Low Rank Representation Algorithm for Subspace Clustering

Low rank representation (LRR) is widely used to construct a good affinity matrix to cluster data drawn from the union of multiple linear subspaces. However, it is not easy to solve the LRR problem in a closed form, and augmented Lagrange multiplier method (ALM) is usually applied. ALM takes a relative long time dealing with the real-world data. To solve the LRR problem efficiently, we propose an efficient low rank representation (eLRR) algorithm. Given a contaminated data set, we propose a novel way to solve the LRR of the data. We establish a useful theorem which directly gives an approximate solution to our LRR optimization problem. Thus, we can construct a good affinity matrix for subspace clustering. Experimental results with several public databases verify the efficiency and effectiveness of our method.