Parametrized Power-Iteration Clustering for Directed Graphs

TL;DR

This paper introduces ParPIC, a scalable clustering method for directed graphs that uses parametrized random walks and automatic diffusion tuning, outperforming traditional spectral methods in accuracy and efficiency.

Contribution

ParPIC is a novel clustering algorithm for directed graphs that incorporates parametrized reversible random walks and automatic diffusion time tuning.

Findings

ParPIC achieves competitive clustering accuracy on synthetic and real-world graphs.

ParPIC offers improved scalability over spectral and teleportation-based methods.

ParPIC produces low-dimensional embeddings with reduced computational complexity.

Abstract

Vertex-level clustering for directed graphs (digraphs) remains challenging as edge directionality breaks the key assumptions underlying popular spectral methods, which also incur the overhead of eigen-decomposition. This paper proposes Parametrized Power-Iteration Clustering (ParPIC), a random-walk-based clustering method for weakly connected digraphs. This builds over the Power-Iteration Clustering paradigm, which uses the rows of the iterated diffusion operator as a data embedding. ParPIC has three important features: the use of parametrized reversible random walk operators, the automatic tuning of the diffusion time, and the efficient truncation of the final embedding, which produces low-dimensional data representations and reduces complexity. Empirical results on synthetic and real-world graphs demonstrate that ParPIC achieves competitive clustering accuracy with improved scalability relative to spectral and teleportation-based methods.