Adaptive distance penalty based nonnegative low-rank representation for semi-supervised learning

Low-rank representation (LRR) aims to find the essential structural information of the original data. It can capture global information and has strong robustness to noise. However, the disadvantage of LRR is that the local similarity of the data is not considered. Most semi-supervised learning (SSL) methods infer unknown tags based on two-stage learning, in which the first stage is a graph construction, and the second stage is to perform SSL for classification. These methods do not share public information that is used to improve classification accuracy. This paper proposes a new semi-supervised learning classification algorithm termed adaptive distance penalty non-negative low-rank representation (ADP-NNLRR). The proposed method combines low rank representation, local constraints and SSL strategy, to make full use of label information and local manifold geometry structure from the data, which in turn, can capture the global subspace, and maintain the relationship between the local parts better. In the proposed method, distance penalty terms and non-negative constraints are introduced, and the obtained low-rank coefficient matrix is used as the similarity matrix of the graph, which can capture more discriminative information for the construction of the graph. Comparative experiments on some classical datasets and noisy datasets verify the superior performance of our proposed method.