The nuclear norm is used to replace the rank function in the subspace clustering algorithm based on low rank representation, it can not estimate the rank of the matrix effectively and it is sensitive to Gauss noise. In this paper, a novel algorithm is proposed to improve the accuracy and maintain its stability under the Gauss noise. When building the objective function, the nuclear norm and Forbenius norm of coefficient matrix are used as the regularization terms, after a strong convex regularizer over singular values of coefficient matrix, an inexact augmented Lagrange multiplier method is utilized to solve the problem. Finally, the affinity matrix is acquired by post-processing of coefficient matrix and the classical spectral clustering method is employed to clustering. The experimental comparison results between the state-of-the-art algorithms on synthetic data, Extended Yale B and PIE datasets demonstrate the effectiveness of the proposed improved method and the robustness to Gauss noise.
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