Low-rank representation with local constraint for graph construction

Abstract

Graph-based semi-supervised learning has been widely researched in recent years. A novel Low-Rank Representation with Local Constraint (LRRLC) approach for graph construction is proposed in this paper. The LRRLC is derived from the original Low-Rank Representation (LRR) algorithm by incorporating the local information of data. Rank constraint has the capacity to capture the global structure of data. Therefore, LRRLC is able to capture both the global structure by LRR and the local structure by the locally constrained regularization term simultaneously. The regularization term is induced by the locality assumption that similar samples have large similarity coefficients. The measurement of similarity among all samples is obtained by LRR in this paper. Considering the non-negativity restriction of the coefficients in physical interpretation, the regularization term can be written as a weighted ℓ1-norm. Then a semi-supervised learning framework based on local and global consistency is used for the classification task. Experimental results show that the LRRLC algorithm provides better representation of data structure and achieves higher classification accuracy in comparison with the state-of-the-art graphs on real face and digit databases.