This paper proposes a novel method called Low-Rank Representation (LRR) for robust subspace clustering and error correction. The goal is to cluster data samples into their respective subspaces while removing outliers and handling errors such as noise, random corruptions, and sample-specific corruptions. LRR seeks the lowest-rank representation of data samples as linear combinations of a given dictionary. It is shown that LRR can exactly recover the row space of the data when the data is clean, and can also recover the row space and detect outliers when the data is contaminated. For data corrupted by arbitrary sparse errors, LRR can approximately recover the row space with theoretical guarantees. Since subspace membership is determined by the row space, LRR can perform robust subspace clustering and error correction efficiently. The method is compared with existing techniques and shown to achieve state-of-the-art performance in applications such as motion segmentation, image segmentation, saliency detection, and face recognition. Theoretical results are provided, showing that LRR can handle various types of errors and recover the true subspace structures. The paper also presents algorithms for subspace segmentation, model estimation, and outlier detection, demonstrating the effectiveness of LRR in handling noisy and corrupted data.This paper proposes a novel method called Low-Rank Representation (LRR) for robust subspace clustering and error correction. The goal is to cluster data samples into their respective subspaces while removing outliers and handling errors such as noise, random corruptions, and sample-specific corruptions. LRR seeks the lowest-rank representation of data samples as linear combinations of a given dictionary. It is shown that LRR can exactly recover the row space of the data when the data is clean, and can also recover the row space and detect outliers when the data is contaminated. For data corrupted by arbitrary sparse errors, LRR can approximately recover the row space with theoretical guarantees. Since subspace membership is determined by the row space, LRR can perform robust subspace clustering and error correction efficiently. The method is compared with existing techniques and shown to achieve state-of-the-art performance in applications such as motion segmentation, image segmentation, saliency detection, and face recognition. Theoretical results are provided, showing that LRR can handle various types of errors and recover the true subspace structures. The paper also presents algorithms for subspace segmentation, model estimation, and outlier detection, demonstrating the effectiveness of LRR in handling noisy and corrupted data.