Sparse Subspace Clustering (SSC) is a method for clustering data points that lie in multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. The approach is based on sparse representation, where each data point can be expressed as a sparse combination of other points in the same subspace. The key idea is that, under mild assumptions, the sparsest representation can be found efficiently using $ \ell_1 $ optimization. This allows for the construction of a similarity matrix, which is then used for spectral clustering to segment the data. SSC can handle noise, outliers, and missing data, making it robust for real-world applications. The method is applied to motion segmentation in video, where it outperforms state-of-the-art methods on 167 video sequences. The algorithm works by first finding sparse representations of data points, then using these representations to build a graph where edges represent similarity between points. Spectral clustering is then applied to this graph to segment the data into subspaces. The method is extended to handle affine subspaces, where points can be represented as affine combinations of other points. It also addresses noisy data by incorporating $ \ell_1 $ minimization with a noise bound. Additionally, the algorithm can handle missing or corrupted data by using sparse representation techniques to reconstruct missing entries and correct outliers. Experiments on the Hopkins 155 motion database show that SSC achieves significantly lower misclassification errors compared to existing methods, particularly for challenging cases like traffic and articulated motion sequences. The method is also robust to missing data and outliers, as demonstrated by experiments on sequences with incomplete or corrupted trajectories. Overall, SSC provides an efficient and effective approach to subspace clustering, with strong performance across various scenarios.Sparse Subspace Clustering (SSC) is a method for clustering data points that lie in multiple low-dimensional linear or affine subspaces embedded in a high-dimensional space. The approach is based on sparse representation, where each data point can be expressed as a sparse combination of other points in the same subspace. The key idea is that, under mild assumptions, the sparsest representation can be found efficiently using $ \ell_1 $ optimization. This allows for the construction of a similarity matrix, which is then used for spectral clustering to segment the data. SSC can handle noise, outliers, and missing data, making it robust for real-world applications. The method is applied to motion segmentation in video, where it outperforms state-of-the-art methods on 167 video sequences. The algorithm works by first finding sparse representations of data points, then using these representations to build a graph where edges represent similarity between points. Spectral clustering is then applied to this graph to segment the data into subspaces. The method is extended to handle affine subspaces, where points can be represented as affine combinations of other points. It also addresses noisy data by incorporating $ \ell_1 $ minimization with a noise bound. Additionally, the algorithm can handle missing or corrupted data by using sparse representation techniques to reconstruct missing entries and correct outliers. Experiments on the Hopkins 155 motion database show that SSC achieves significantly lower misclassification errors compared to existing methods, particularly for challenging cases like traffic and articulated motion sequences. The method is also robust to missing data and outliers, as demonstrated by experiments on sequences with incomplete or corrupted trajectories. Overall, SSC provides an efficient and effective approach to subspace clustering, with strong performance across various scenarios.