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arXiv · 2210.00310

Parametrized Power-Iteration Clustering for Directed Graphs

Gwendal Debaussart-Joniec·Harry Sevi·Matthieu Jonckheere·Argyris Kalogeratos
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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.

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Gwendal Debaussart-Joniec, Harry Sevi, Matthieu Jonckheere, Argyris Kalogeratos. 2022-10-01. Parametrized Power-Iteration Clustering for Directed Graphs. https://arxiv.org/abs/2210.00310

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