Semi-supervised learning algorithm based on non-negative low rank and sparse graph can not describe the structures of the data exactly. Therefore, an improved algorithm which integrates smoothed low rank representation and weighted sparsity constraint is proposed. The low rank term and sparse term of the classical algorithm are improved by this algorithm respectively, and the global subspace structure and the locally linear structure can be captured exactly. When building the objective function, the logarithm determinant function instead of the nuclear norm is used to approximate the rank function smoothly. Meanwhile, the shape interaction information and the label information of labeled samples is used to build the weighted sparsity constraint regularization term. Then, the objective function is solved by a linearized alternating direction method with adaptive penalty and the graph construction is restructured by an available post-processing method. Finally, a semi-supervised classification framework based on local and global consistency is used to finish the learning task. The experimental results on ORL, Extended Yale B and USPS database show that the improved algorithm improves the accuracy of semi-supervised learning.
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