SSC-l0: Sparse Subspace Clustering with the l0 Inequality Constraint

Self-expression learning methods often obtain a coefficient matrix to measure the similarity between pairs of samples. However, directly using all points to represent a fixed sample in a class under the self-expression framework may not be ideal, as points from other classes participate in the representing process. To alleviate this issue, this study attempts to achieve representation learning between points only coming from the same class. In practice, it is easier for data points from the same class to represent each other than that from different classes. So, when reconstructing a point, if the number of non-zero elements in the coefficient vector is limited, a model is more likely to select data points from the class where the reconstructed point lies to complete the reconstruction work. Based on this idea, we propose Sparse Subspace Clustering with the l 0 inequality constraint (SSC- l 0 ). In SSC- l 0 , the l 0 inequality constraint determines the maximum number of non-zero elements in the coefficient vector, which helps SSC- l 0 to conduct representation learning among the points in the same class. After introducing the simplex constraint to ensure the translation invariance of the model, an optimization method concerning l 0 inequality constraint is formed to solve the proposed SSC- l 0 , and its convergence is theoretically analyzed. Extensive experiments on well-known datasets demonstrate the superiority of SSC- l 0 compared to several state-of-the-art methods.