2017/06/19 by Di Wang, Wang, Di, Kimon Fountoulakis +7 · 1 citation
Computer Science · Physics and Astronomy · #Advanced Clustering Algorithms Research #Artificial Intelligence (cs.AI) #Complex Network Analysis Techniques #Data Structures and Algorithms (cs.DS) #FOS: Computer and information sciences #Information Retrieval (cs.IR) #Topological and Geometric Data Analysis #cs.AI #cs.DS #cs.IR
paper · pdf · doi:10.48550/arxiv.1706.05826
Appeared in ICML 2017. Current version added reference and discussion of work on generalized Cheeger's inequalities
openalex publication_date 2017/06/19 · arxiv created 2018/06/10 · arxiv updated 2018/06/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Diffusions and related random walk procedures are of central importance in many areas of machine learning, data analysis, and applied mathematics. Because they spread mass agnostically at each step in an iterative manner, they can sometimes spread mass "too aggressively," thereby failing to find the "right" clusters. We introduce a novel Capacity Releasing Diffusion (CRD) Process, which is both faster and stays more local than the classical spectral diffusion process. As an application, we use our CRD Process to develop an improved local algorithm for graph clustering. Our local graph clustering method can find local clusters in a model of clustering where one begins the CRD Process in a cluster whose vertices are connected better internally than externally by an O(log2 n) factor, where n is the number of nodes in the cluster. Thus, our CRD Process is the first local graph clustering algorithm that is not subject to the well-known quadratic Cheeger barrier. Our result requires a certain smoothness condition, which we expect to be an artifact of our analysis. Our empirical evaluation demonstrates improved results, in particular for realistic social graphs where there are moderately good---but not very good---clusters.