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Consider a set of data points generated from various linear subspaces. Subspace segmentation tasks, which are important in fields such as computer vision and image processing, aim to partition the set of data points so as to recover these subspaces. The subspace segmentation method, fixed rank representation (FRR), was introduced to remedy the problem of insufficient sampling in classical low rank representation (LRR). In many subspace segmentation applications, FRR has achieved much better results than those of LRR. In this paper, a new FRR-related algorithm, called self-regularized fixed rank representation (SRFRR), is proposed. In SRFRR, a Laplacian regularizer is constructed using the coefficient matrix obtained by SRFRR itself. Further, by proving that the Laplacian regularizer can be transformed into a structure constraint on the coefficient matrix, we show that another existing method, sparse FRR …