# p-Norm Flow Diffusion for Local Graph Clustering

@article{Yang2020pNormFD, title={p-Norm Flow Diffusion for Local Graph Clustering}, author={Shenghao Yang and Di Wang and Kimon Fountoulakis}, journal={ArXiv}, year={2020}, volume={abs/2005.09810} }

Local graph clustering and the closely related seed set expansion problem are primitives on graphs that are central to a wide range of analytic and learning tasks such as local clustering, community detection, nodes ranking and feature inference. Prior work on local graph clustering mostly falls into two categories with numerical and combinatorial roots respectively. In this work, we draw inspiration from both fields and propose a family of convex optimization formulations based on the idea of…

## 16 Citations

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### Weighted flow diffusion for local graph clustering with node attributes: an algorithm and statistical guarantees

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This work presents a simple local graph clustering algorithm for graphs with node attributes, based on the idea of using mass locally in the graph while accounting for both structural and attribute proximities, and shows that incorporating node attributes leads to superior local clustering performances using real-world graph datasets.

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### 2-norm Flow Diffusion in Near-Linear Time

- Computer Science2021 IEEE 62nd Annual Symposium on Foundations of Computer Science (FOCS)
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An near-linear time randomized algorithm for the 2-norm flow diffusion problem, a recently proposed diffusion model based on network flow with demonstrated graph clustering related applications both in theory and in practice.

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This work presents a novel direct multiway spectral clustering algorithm in the p -norm, a nonlinear generalization of the standard graph Laplacian, recasted as an unconstrained minimization problem on a Grassmann manifold, and demonstrates the effectiveness and accuracy of the algorithm in various artificial test-cases.

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