Graph Representation Learning with Motif Structures

Graphs are important data structures that can be found in a wide variety of real-world scenarios. It is well recognised that the primitive graph representation is sparse, high- dimensional and noisy. Therefore, it is challenging to analyse such primitive data for downstream graph-related tasks (e.g., community detection and node classification). Graph representation learning (GRL) aims to map graph data into a low-dimensional dense vector space in which the graph information is maximally preserved. It allows primitive graphs to be easily analysed in the new mapped vector space.
GRL methods typically focus on simple connectivity patterns that only explicitly model relations between two nodes. Motif structures that capture relations among three or more nodes have been recognised as functional units of graphs, and can gain new insights into the organisation of graphs. Therefore, in this thesis we propose new GRL methods modelling motif structures for different graph-related tasks and applications along three directions: (1) a method to learn a spectral embedding space with both edge-based and triangle-based structures for clustering nodes; (2) a graph transformer by unifying homophily and heterophily representation for role classification and motif structure completion; (3) a method to tackle noises in knowledge graph representations with motif structures for recommendations and knowledge graph completion. Experimental studies show that the proposed methods have outperformed related state-of-the-art methods for targeted tasks and applications.