Graph Max Shift: A Hill-Climbing Method for Graph Clustering

TL;DR

This paper introduces Graph Max Shift, a hill-climbing algorithm for graph clustering that iteratively moves nodes to neighbors with higher degrees, demonstrating asymptotic consistency on certain random geometric graphs.

Contribution

The paper proposes a novel graph clustering method inspired by gradient ascent, with theoretical proof of asymptotic consistency under specific conditions.

Findings

Method is asymptotically consistent on random geometric graphs.

Algorithm effectively identifies density-based clusters.

The approach extends gradient ascent ideas to graph structures.

Abstract

We present a method for graph clustering that is analogous to gradient ascent methods previously proposed for clustering points in space. The algorithm, which can be viewed as a max-degree hill-climbing procedure on the graph, iteratively moves each node to a neighboring node of highest degree. We show that, when applied to a random geometric graph whose nodes correspond to data drawn i.i.d. from a density with Morse regularity, the method is asymptotically consistent. Here, consistency is in the sense of Fukunaga and Hostetler, meaning, with respect to the partition of the support of the density defined by the basins of attraction of the density gradient flow.