Local Manifold Graphs Based on Low-Rank Representation for Semi-supervised Learning

Graphs can be applied to graph-based semi-supervised learning and play an important role in data classification tasks. A good graph can reveal the underlying relationships between data and capture hidden structural information. This paper proposes a Low- Rank Representation with Local Manifold (LRRLM) method for graph construction. Low-Rank Representation (LRR) can capture the global structure of data. For capturing the local structure of data, a local constraint term, which utilizes distance metrics to weight the representation coefficients, is integrated into the LRR framework. Furthermore, manifold regularization is also introduced to describe the manifold information between data using the K-nearest neighbors method. An efficient linearized alternating direction technique with adaptive penalty is developed to solve the proposed LRRLM problem. Based on the representation coefficients obtained by the LRRLM, a weighted graph is constructed for semi-supervised classification tasks. Experimental results on some public datasets show that the proposed LRRLM method can build a more discriminative graph and can achieve higher classification accuracy when compared with existing state-of-the-art graph construction methods. Moreover, the LRRLM graph is robust to noise and occlusions that could occur in real-world applications.