Parametrized Power-Iteration Clustering for Directed Graphs

Gwendal Debaussart-Joniec, Harry Sevi, Matthieu Jonckheere, Argyris Kalogeratos
Proceedings of the 43rd International Conference on Machine Learning, PMLR 306:23432-23455, 2026.

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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v306-debaussart-joniec26a, title = {Parametrized Power-Iteration Clustering for Directed Graphs}, author = {Debaussart-Joniec, Gwendal and Sevi, Harry and Jonckheere, Matthieu and Kalogeratos, Argyris}, booktitle = {Proceedings of the 43rd International Conference on Machine Learning}, pages = {23432--23455}, year = {2026}, editor = {Zhang, Tong and Dudik, Miroslav and Jaggi, Martin and Agarwal, Alekh and Li, Sharon and Schuurmans, Dale and Zhu, Jerry and Berkenkamp, Felix and Dong, Hanze and Bietti, Alberto}, volume = {306}, series = {Proceedings of Machine Learning Research}, month = {06--11 Jul}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/v306/main/assets/debaussart-joniec26a/debaussart-joniec26a.pdf}, url = {https://proceedings.mlr.press/v306/debaussart-joniec26a.html}, 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.} }
Endnote
%0 Conference Paper %T Parametrized Power-Iteration Clustering for Directed Graphs %A Gwendal Debaussart-Joniec %A Harry Sevi %A Matthieu Jonckheere %A Argyris Kalogeratos %B Proceedings of the 43rd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2026 %E Tong Zhang %E Miroslav Dudik %E Martin Jaggi %E Alekh Agarwal %E Sharon Li %E Dale Schuurmans %E Jerry Zhu %E Felix Berkenkamp %E Hanze Dong %E Alberto Bietti %F pmlr-v306-debaussart-joniec26a %I PMLR %P 23432--23455 %U https://proceedings.mlr.press/v306/debaussart-joniec26a.html %V 306 %X 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.
APA
Debaussart-Joniec, G., Sevi, H., Jonckheere, M. & Kalogeratos, A.. (2026). Parametrized Power-Iteration Clustering for Directed Graphs. Proceedings of the 43rd International Conference on Machine Learning, in Proceedings of Machine Learning Research 306:23432-23455 Available from https://proceedings.mlr.press/v306/debaussart-joniec26a.html.

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