Corpus ID: 231985774

Co-clustering Vertices and Hyperedges via Spectral Hypergraph Partitioning

@article{Zhu2021CoclusteringVA,
  title={Co-clustering Vertices and Hyperedges via Spectral Hypergraph Partitioning},
  author={Yu Zhu and Boning Li and Santiago Segarra},
  journal={ArXiv},
  year={2021},
  volume={abs/2102.10169}
}
We propose a novel method to co-cluster the vertices and hyperedges of hypergraphs with edge-dependent vertex weights (EDVWs). In this hypergraph model, the contribution of every vertex to each of its incident hyperedges is represented through an edge-dependent weight, conferring the model higher expressivity than the classical hypergraph. In our method, we leverage random walks with EDVWs to construct a hypergraph Laplacian and use its spectral properties to embed vertices and hyperedges in a… Expand

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References

SHOWING 1-10 OF 39 REFERENCES
Inhomogeneous Hypergraph Clustering with Applications
TLDR
It is proved that inhomogenous partitioning produces a quadratic approximation to the optimal solution if the inhomogeneous costs satisfy submodularity constraints and offers significant performance improvements in applications such as structure learning of rankings, subspace segmentation and motif clustering. Expand
Beyond pairwise clustering
TLDR
A two-step algorithm is proposed for solving the problem of clustering in domains where the affinity relations are not dyadic (pairwise), but rather triadic, tetradic or higher, which is an instance of the hypergraph partitioning problem. Expand
Random Walks on Hypergraphs with Edge-Dependent Vertex Weights
TLDR
This paper uses random walks to develop a spectral theory for hypergraphs with edge-dependent vertex weights, and derives a random walk-based hypergraph Laplacian, and bound the mixing time of random walks on such hyper graphs. Expand
Learning with Hypergraphs: Clustering, Classification, and Embedding
TLDR
This paper generalizes the powerful methodology of spectral clustering which originally operates on undirected graphs to hypergraphs, and further develop algorithms for hypergraph embedding and transductive classification on the basis of the spectral hypergraph clustering approach. Expand
Community Detection for Hypergraph Networks via Regularized Tensor Power Iteration
To date, social network analysis has been largely focused on pairwise interactions. The study of higher-order interactions, via a hypergraph network, brings in new insights. We study communityExpand
Heterogeneous Hyper-Network Embedding
TLDR
A fully-connected and graph convolutional layers are designed to project different types of nodes into a common low-dimensional space, a tuple-wise similarity function is proposed to preserve the network structure, and a ranking based loss function is used to improve the similarity scores of hyperedges in the embedding space. Expand
Probabilistic graph and hypergraph matching
  • R. Zass, A. Shashua
  • Mathematics, Computer Science
  • 2008 IEEE Conference on Computer Vision and Pattern Recognition
  • 2008
TLDR
This work formalizes a soft matching criterion that emerges from a probabilistic interpretation of the problem input and output, as opposed to previous methods that treat soft matching as a mere relaxation of the hard matching problem. Expand
A Provable Generalized Tensor Spectral Method for Uniform Hypergraph Partitioning
TLDR
This paper develops a unified approach for partitioning uniform hypergraphs by means of a tensor trace optimization problem involving the affinity tensor, and a number of existing higher-order methods turn out to be special cases of the proposed formulation. Expand
Co-clustering documents and words using bipartite spectral graph partitioning
  • I. Dhillon
  • Computer Science, Mathematics
  • KDD '01
  • 2001
TLDR
A new spectral co-clustering algorithm is used that uses the second left and right singular vectors of an appropriately scaled word-document matrix to yield good bipartitionings and it can be shown that the singular vectors solve a real relaxation to the NP-complete graph bipartitionsing problem. Expand
The Fiedler Vector of a Laplacian Tensor for Hypergraph Partitioning
TLDR
A feasible optimization algorithm to compute the Fiedler vector according to the normalized Laplacian tensor of an even-uniform hypergraph and a novel tensor-based spectral method for partitioning vertices of the hypergraph are developed. Expand
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