On Learning the Structure of Clusters in Graphs

TL;DR

This paper investigates the problem of learning the high-level structure of clusters in graphs and hypergraphs, introducing new algorithms that are both theoretically sound and practically effective across diverse real-world datasets.

Contribution

It presents four novel algorithms for efficiently learning cluster structures in graphs and hypergraphs, addressing a gap in existing methods that overlook high-level structures.

Findings

Algorithms are practical and effective on synthetic datasets.

Algorithms perform well on real-world datasets including images and networks.

Experimental results show immediate applicability in various domains.

Abstract

Graph clustering is a fundamental problem in unsupervised learning, with numerous applications in computer science and in analysing real-world data. In many real-world applications, we find that the clusters have a significant high-level structure. This is often overlooked in the design and analysis of graph clustering algorithms which make strong simplifying assumptions about the structure of the graph. This thesis addresses the natural question of whether the structure of clusters can be learned efficiently and describes four new algorithmic results for learning such structure in graphs and hypergraphs. All of the presented theoretical results are extensively evaluated on both synthetic and real-word datasets of different domains, including image classification and segmentation, migration networks, co-authorship networks, and natural language processing. These experimental results demonstrate that the newly developed algorithms are practical, effective, and immediately applicable for learning the structure of clusters in real-world data.