ALG: Adaptive low-rank graph regularization for scalable semi-supervised and unsupervised learning

Abstract

Graph-based semi-supervised learning (SSL) is one of the most popular topics in the past decades. Most graph-based SSL methods utilize two stage-approach to infer the class labels of the unlabeled data, where the first stage is to construct a graph in an unsupervised way for characterizing the geometry of data manifold while the second stage is to perform SSL for classification. However, the graph construction and SSL stages are usually separate. They do not share any common information to enhance the performance of classification. In this paper, we aim to solve the above problem by proposing a unified framework for SSL. In detail, we first adopt an adaptive low-rank model for graph construction, where the coefficient matrix is calculated through an efficient procedure so that the corresponding constructed graph can capture the global structure of data manifold. Meriting from such a graph, we then propose a unified framework for SSL, where we have involved the graph construction, the SSL strategy into the whole objective function. As a result, the class labels learned by SSL can provide more discriminative information for graph construction, while the updated graph can further enhance the classification accuracies of SSL. Simulation indicates that the proposed method can achieve better classification performance compared with other state-of-the-art graph-based methods.