Data-driven graph construction and graph learning: A review

A graph is one of important mathematical tools to describe ubiquitous relations. In the classical graph theory and some applications, graphs are generally provided in advance, or can at least be defined clearly. Thus, the main focus is to measure/analyze the graphs for mining informative patterns. However, for many real-world scenarios, the graph is often uncertain due to the fact that data associated with the vertices in the graph are high-dimensional, noisy, differently distributed, and even no clear definition. As a result, one needs to design or learn graphs from data prior to any analysis, which in turn affects the subsequent tasks. Therefore, constructing a high-quality graph has become an increasingly hot research problem, which inspired many graph construction methods being proposed in the past years. Since there has been no systematic summary on this topic, in this paper, we review the main-stream graph construction/learning methods involved in both general machine learning algorithms (including semi-supervised learning, clustering, manifold learning, and spectral kernel learning, etc.) and some specific applications (especially, the modeling and analysis of functional brain connectivity). Additionally, we introduce a matrix-regularized graph learning framework that can benefit to unify some existing graph construction models and develop new graph learning algorithms. Finally, we discuss several related topics and some promising research directions in this field.