Graph Based Semi-Supervised Learning via Structure Preserving Low-Rank Representation

摘要

Semi-supervised learning works on utilizing both labeled and unlabeled data to improve learning performance, which has been receiving increasing attention in many applications such as clustering and classification. In this paper, we focus on the semi-supervised learning methods developed on data graph whose edge weights are measured by low-rank representation (LRR) coefficients. Specifically, we impose two constraints on LRR when constructing the graph: local affinity and distant repulsion, to preserve the data manifold information. The proposed model, termed structure preserving LRR (SPLRR), can preserve the local geometrical structure and without distorting the distant repulsion property. Using the augmented Lagrange multiplier (ALM) method framework, we derive an efficient approach to optimizing the SPLRR model. Experiments are conducted on four widely used data sets to validate the effectiveness of our proposed SPLRR model and the results demonstrate that SPLRR is an excellent model for graph based semi-supervised learning in comparison with the state-of-the-art methods.