Hypergraph Clustering Based on PageRank

Takai, Yuuki; Miyauchi, Atsushi; Ikeda, Masahiro; Yoshida, Yuichi

doi:10.1145/3394486.3403248

Cited by 41 publications

(29 citation statements)

References 20 publications

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“…The term δ is the additional cost that we pay for performing graph reduction. The dependence on δ essentially generalizes the previous works that analyzed the conductance with only all-ornothing penalty [25,31], as our result matches these when δ = 1. But our method gives the flexibility to choose other values δ e and while δ in the worst case could be as large as |e |/2, in practice, δ can be chosen much smaller (See §7).…”

Section: Local Conductance Approximationsupporting

confidence: 87%

“…First, Li et al [25] defined a quadratic hypergraph PageRank by directly using Lovász extension of the splitting function f e to control the diffusion instead of a reduction. Both Li et al [25] and Takai et al [31] simultaneously proved that this PageRank can be used to partition hypergraphs with an all-or-nothing penalty and a Cheeger-type guarantee. Neither approach gives a strongly local algorithm and they have complexity…”

Section: Directly Related Workmentioning

confidence: 99%

“…The specific problem we address is a mincut-inspired hypergraph generalization of personalized PageRank along with a strongly local algorithm to rapidly approximate solutions. Our formulation differs in a number of important ways from existing Laplacian [43] and quadratic function-based hypergraph PageRank generalizations [25,27,31].…”

Section: Introductionmentioning

confidence: 99%

“…We investigate a series of different algorithms that will identify a cluster nearby a seed node in a hypergraph: (1) Andersen-Chung-Lang PageRank on the star and clique expansion of the hypergraph (ACL-Star, ACL-Clique, respectively), these algorithms are closely related to ideas proposed in [1,43]; (2) HyperLocal, a recent maximum flow-based hypergraph clustering algorithm [33]; (3) quadratic hypergraph PageRank [25,31] (which is also closely related to [15]), and (4) our Local Hypergraph-PageRank (LHPR). These are all strongly local except for (3), which we include because our algorithm LHPR is essentially the strongly local analogue of (3).…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning

Liu¹,

Veldt

Song³

et al. 2021

Proceedings of the Web Conference 2021

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Hypergraph-based machine learning methods are now widely recognized as important for modeling and using higher-order and multiway relationships between data objects. Local hypergraph clustering and semi-supervised learning specifically involve finding a well-connected set of nodes near a given set of labeled vertices. Although many methods for local graph clustering exist, there are relatively few for localized clustering in hypergraphs. Moreover, those that exist often lack flexibility to model a general class of hypergraph cut functions or cannot scale to large problems. To tackle these issues, this paper proposes a new diffusion-based hypergraph clustering algorithm that solves a quadratic hypergraph cut based objective akin to a hypergraph analog of Andersen-Chung-Lang personalized PageRank clustering for graphs. We prove that, for graphs with fixed maximum hyperedge size, this method is strongly local, meaning that its runtime only depends on the size of the output instead of the size of the hypergraph and is highly scalable. Moreover, our method enables us to compute with a wide variety of cardinality-based hypergraph cut functions. We also prove that the clusters found by solving the new objective function satisfy a Cheeger-like quality guarantee. We demonstrate that on large real-world hypergraphs our new method finds better clusters and runs much faster than existing approaches. Specifically, it runs in a few seconds for hypergraphs with a few million hyperedges compared with minutes for a flow-based technique. We furthermore show that our framework is general enough that can also be used to solve other p-norm based cut objectives on hypergraphs. CCS CONCEPTS• Mathematics of computing → Hypergraphs; • Theory of computation → Semi-supervised learning; • Computing methodologies → Cluster analysis.

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Section: Local Conductance Approximationsupporting

confidence: 87%

Section: Directly Related Workmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning

Liu¹,

Veldt

Song³

et al. 2021

Proceedings of the Web Conference 2021

View full text Add to dashboard Cite

show abstract

“…Besides, some researches utilize hypergraph regularization term, rather than pairwise ones, to infer the complex relationships between genes [3]. Although the above methods achieve strong performance, they suffer from the size and construction of the hypergraph [4,5].…”

Section: Related Workmentioning

confidence: 99%

Multi-View Clustering Through Self-Weighted High-Order Similarity Fusion

Peng

Cai

2021

2021 IEEE International Conference on Multimedia and Expo (ICME)

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Recently, multi-view clustering methods based on high-order sample affinities to ease learning complex structures attract much attention. However, most of the methods used predefined similarity, which is easy to be corrupted by noises and yield suboptimal performance. To tackle with this issue, this paper proposes a novel multi-view clustering method, named by WHSF, which seeks to learn a self-weighted high-order similarity. The high-order similarity is formulated to flexibly capture the intrinsic structure of data, characterized by fusing the interactions across views. A high-order regularization based on the defined similarity is incorporated into the model and assigned with weight parameters, enabling the model to focus on mutual information among views. Extensive experiments on four real-world datasets show that the proposed WHSF outperforms benchmark multi-view methods and can reveal a reliable structure concealed across multiple views.

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Nonlinear evolution equation associated with hypergraph Laplacian

Ikeda

Uchida

2023

Math Methods in App Sciences

Self Cite

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Let V be a finite set, E ⊂ 2 V be a set of hyperedges, and w ∶ E → (0, ∞) be an edge weight. On the (wighted) hypergraph G = (V, E, w), we can define a multivalued nonlinear operator L G,p (p ∈ [1, ∞)) as the subdifferential of a convex function on R V , which is called "hypergraph p-Laplacian." In this article, we first introduce an inequality for this operator L G,p , which resembles the Poincaré-Wirtinger inequality in PDEs. Next, we consider an ordinary differential equation on R V governed by L G,p , which is referred as "heat" equation on the graph and used to study the geometric structure of the hypergraph in recent researches. With the aid of the Poincaré-Wirtinger type inequality, we can discuss the existence and the large time behavior of solutions to the ODE by procedures similar to those for the standard heat equation in PDEs with the zero Neumann boundary condition.

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Hypergraph Clustering Based on PageRank

Cited by 41 publications

References 20 publications

Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning

Strongly Local Hypergraph Diffusions for Clustering and Semi-supervised Learning

Multi-View Clustering Through Self-Weighted High-Order Similarity Fusion

Nonlinear evolution equation associated with hypergraph Laplacian

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