Understanding Accelerated Graph Clustering via Local Grouping

Local grouping is a commonly used technique to scale application size in machine learning domains, such as image segmentation, graph representation learning, and multidimensional clustering. Those applications usually model their data using a graph. Local grouping is conducted in different heuristics by combining neighboring graph nodes. Therefore, the graph becomes coarser and less computational demanding for clustering. Success is claimed by achieving similar performance with less computation resource or scaling the application size by several magnitudes larger. However, no theoretical study has been conducted to understand the impact of the choice of local grouping heuristics in clustering quality. In this work, we will try to address this gap in mathematical analysis and provide suggestions for practical applications.