Robust Subspace Segmentation by Low-Rank Representation

We propose low-rank representation (LRR) to segment data drawn from a union of mul- tiple linear (or a-ne) subspaces. Given a set of data vectors, LRR seeks the lowest- rank representation among all the candidates that represent all vectors as the linear com- bination of the bases in a dictionary. Unlike the well-known sparse representation (SR), which computes the sparsest representation of each data vector individually, LRR aims at flnding the lowest-rank representation of a collection of vectors jointly. LRR better cap- tures the global structure of data, giving a more efiective tool for robust subspace seg- mentation from corrupted data. Both the- oretical and experimental results show that LRR is a promising tool for subspace segmen- tation.