Graph-based semi-supervised learning method has been influential in the data mining and machine learning fields. The key is to construct an effective graph to capture the intrinsic data structure, which further benefits for propagating the un-labeled data over the graph. The existing methods have shown the effectiveness of a graph regularization term on measuring the similarities among samples, which further uncovers the data structure. However, all the existing graph-based methods are on the sample-level, i.e. calculate the similarity based on sample-level representation coefficients, inevitably overlooking the underlying part-level structure within sample. Inspired by the strong interpretability of Non-negative Matrix Factorization (NMF) method, we design a more robust and discriminative graph, by integrating low-rank factorization and graph regularizer into a unified framework. Specifically, a novel low-rank factorization through Semi-Non-negative Matrix Factorization (SNMF) is proposed to extract the semantically part-level representation. Moreover, instead of incorporating a graph regularization on sample-level, we propose a sparse graph regularization term built on the decomposed part-level representation. This practice results in a more accurate measurement among samples, generating a more discriminative graph for semi-supervised learning. As a non-trivial contribution, we also provide an optimization solution to the proposed method. Comprehensive experimental evaluations show that our proposed method is able to achieve superior performance compared with the state-of-the-art semi-supervised classification baselines in both transductive and inductive scenarios.
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