Robust Subspace Segmentation by Low-Rank Representation

TLDR

LRR differs from sparse representation by seeking a lowest‑rank representation of all vectors jointly rather than the sparsest per vector. The authors propose low‑rank representation to segment data drawn from a union of multiple linear or affine subspaces. LRR seeks the lowest‑rank representation of all data vectors by expressing each as a linear combination of dictionary bases. LRR better captures global data structure and, according to theory and experiments, proves to be a promising tool for robust subspace segmentation of corrupted data.

Abstract

We propose low-rank representation (LRR) to segment data drawn from a union of multiple linear (or affine) subspaces. Given a set of data vectors, LRR seeks the lowest-rank representation among all the candidates that represent all vectors as the linear combination 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 finding the lowest-rank representation of a collection of vectors jointly. LRR better captures the global structure of data, giving a more effective tool for robust subspace segmentation from corrupted data. Both theoretical and experimental results show that LRR is a promising tool for subspace segmentation.