  Semi-supervised learning (SSL) has tremendous value in practice due to its
ability to utilize both labeled data and unlabelled data. An important class of
SSL methods is to naturally represent data as graphs such that the label
information of unlabelled samples can be inferred from the graphs, which
corresponds to graph-based semi-supervised learning (GSSL) methods. GSSL
methods have demonstrated their advantages in various domains due to their
uniqueness of structure, the universality of applications, and their
scalability to large scale data. Focusing on this class of methods, this work
aims to provide both researchers and practitioners with a solid and systematic
understanding of relevant advances as well as the underlying connections among
them. This makes our paper distinct from recent surveys that cover an overall
picture of SSL methods while neglecting fundamental understanding of GSSL
methods. In particular, a major contribution of this paper lies in a new
generalized taxonomy for GSSL, including graph regularization and graph
embedding methods, with the most up-to-date references and useful resources
such as codes, datasets, and applications. Furthermore, we present several
potential research directions as future work with insights into this rapidly
growing field.
