The paper introduces a novel method called Low-Rank Representation (LRR) for subspace segmentation, which aims to segment data drawn from multiple linear or affine subspaces. Unlike sparse representation (SR), which seeks the sparsest representation of each data vector individually, LRR finds the lowest-rank representation of all vectors jointly, better capturing the global structure of the data. This makes LRR more effective for robust subspace segmentation, especially in the presence of corrupted data. The method is theoretically grounded and experimentally validated, showing superior performance compared to existing methods such as GPCA, LSA, RANSAC, and SSC. LRR is particularly effective in handling corrupted data, as demonstrated through various experiments on toy data, slightly corrupted data, and heavily corrupted data. The paper also discusses future directions, including learning a compact dictionary for LRR and exploring its applications beyond subspace segmentation.The paper introduces a novel method called Low-Rank Representation (LRR) for subspace segmentation, which aims to segment data drawn from multiple linear or affine subspaces. Unlike sparse representation (SR), which seeks the sparsest representation of each data vector individually, LRR finds the lowest-rank representation of all vectors jointly, better capturing the global structure of the data. This makes LRR more effective for robust subspace segmentation, especially in the presence of corrupted data. The method is theoretically grounded and experimentally validated, showing superior performance compared to existing methods such as GPCA, LSA, RANSAC, and SSC. LRR is particularly effective in handling corrupted data, as demonstrated through various experiments on toy data, slightly corrupted data, and heavily corrupted data. The paper also discusses future directions, including learning a compact dictionary for LRR and exploring its applications beyond subspace segmentation.