# Parametrized Power-Iteration Clustering for Directed Graphs

arXiv: https://arxiv.org/abs/2210.00310 · HTML: https://mlsanity.com/paper/2210.00310/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 26 references that are in the map.
- First posted on arXiv 1 Oct 2022.

## Builds on (most cited first, 8 of 8)

- [Hermitian matrices for clustering directed graphs: insights and applications](https://mlsanity.com/paper/1908.02096/) (2019)
- [Higher-Order Spectral Clustering of Directed Graphs](https://mlsanity.com/paper/2011.05080/) (2020)
- [Learning by Unsupervised Nonlinear Diffusion](https://mlsanity.com/paper/1810.06702/) (2018)
- [An Introduction to Johnson-Lindenstrauss Transforms](https://mlsanity.com/paper/2103.00564/) (2021)
- [Multimodal Data Visualization and Denoising with Integrated Diffusion](https://mlsanity.com/paper/2102.06757/) (2021)
- [Diffusion Maps : Using the Semigroup Property for Parameter Tuning](https://mlsanity.com/paper/2203.02867/) (2022)
- [Generalized Dirichlet Energy and Graph Laplacians for Clustering Directed and Undirected Graphs](https://mlsanity.com/paper/2203.03221/) (2022)
- [A Tutorial on the Spectral Theory of Markov Chains](https://mlsanity.com/paper/2207.02296/) (2022)

## Built on by (most cited first, 1 of 1)

- [Multi-view diffusion geometry using intertwined diffusion trajectories](https://mlsanity.com/paper/2512.01484/) (2025)

## Abstract (arXiv)

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.