This paper addresses the subspace clustering problem, aiming to cluster data samples into their respective subspaces while removing outliers. The proposed method, Low-Rank Representation (LRR), seeks the lowest-rank representation of the data samples as linear combinations of bases in a given dictionary. LRR is shown to solve the subspace clustering problem effectively: it exactly recovers the true subspace structures when the data is clean, can recover the row space and detect outliers when the data is contaminated by outliers, and can approximately recover the row space with theoretical guarantees when the data is corrupted by arbitrary sparse errors. The subspace membership is determined by the row space, making LRR capable of robust subspace clustering and error correction. The paper also discusses related methods and provides theoretical analysis to support the effectiveness of LRR.This paper addresses the subspace clustering problem, aiming to cluster data samples into their respective subspaces while removing outliers. The proposed method, Low-Rank Representation (LRR), seeks the lowest-rank representation of the data samples as linear combinations of bases in a given dictionary. LRR is shown to solve the subspace clustering problem effectively: it exactly recovers the true subspace structures when the data is clean, can recover the row space and detect outliers when the data is contaminated by outliers, and can approximately recover the row space with theoretical guarantees when the data is corrupted by arbitrary sparse errors. The subspace membership is determined by the row space, making LRR capable of robust subspace clustering and error correction. The paper also discusses related methods and provides theoretical analysis to support the effectiveness of LRR.