Semi-supervised sparse subspace clustering with manifold regularization

For sparse subspace clustering methods, it is crucial to develop a good representation matrix to capture the data structure. In this paper, we incorporated the label information into sparse representation and proposed a new semi-supervised sparse subspace clustering method, named semi-supervised sparse subspace clustering with manifold regularization (S \(^4\) ${}^4$ CMR). When developing the sparse self-expressive matrix, the S \(^4\) ${}^4$ CMR method utilized the label information to constrain the development of expressiveness coefficients. The local manifold regularization was also integrated to enhance clustering stability and local consistency. By utilizing the Alternating Direction Method of Multipliers (ADMM), the convex optimization problem associated with linear constraints can be easily resolved. The developed similarity matrix can provide strong discriminant information, making it more effective for semi-supervised tasks. The effectiveness of the proposed algorithm is demonstrated through experiments on benchmark data sets, such as motion segmentation and image clustering.