Sparse Subspace Clustering (SSC) is a method for clustering data points that lie in a union of low-dimensional subspaces. The key idea is that each data point can be represented as a sparse combination of other points from the same subspace. This leads to solving a sparse optimization problem, which is then used in a spectral clustering framework to infer the clustering of the data. The algorithm is efficient and can handle data points near the intersections of subspaces. It also directly addresses data nuisances such as noise, sparse outliers, and missing entries by incorporating these into the optimization program. The method is tested on synthetic data and real-world problems like motion segmentation and face clustering, showing superior performance compared to existing methods. Theoretical analysis supports the algorithm's ability to recover subspace-sparse representations under certain conditions on subspace arrangements and data distribution. The algorithm is robust to errors and can handle both linear and affine subspaces.Sparse Subspace Clustering (SSC) is a method for clustering data points that lie in a union of low-dimensional subspaces. The key idea is that each data point can be represented as a sparse combination of other points from the same subspace. This leads to solving a sparse optimization problem, which is then used in a spectral clustering framework to infer the clustering of the data. The algorithm is efficient and can handle data points near the intersections of subspaces. It also directly addresses data nuisances such as noise, sparse outliers, and missing entries by incorporating these into the optimization program. The method is tested on synthetic data and real-world problems like motion segmentation and face clustering, showing superior performance compared to existing methods. Theoretical analysis supports the algorithm's ability to recover subspace-sparse representations under certain conditions on subspace arrangements and data distribution. The algorithm is robust to errors and can handle both linear and affine subspaces.