New method clusters hypergraphs using weighted random walks and Laplacians.
problem Clustering hypergraph data with edge-dependent weights.
method Random walks with edge-dependent vertex weights, constructing hypergraph Laplacians for clustering.
result Proposed methods outperform existing hypergraph clustering algorithms.
Perfect clustering achieved in hypergraphs with enough interactions.
problem Complexity and lack of tractable models for analyzing hypergraphs.
method Introduced an interaction hypergraph model for analyzing hypergraphs, defined latent embeddings, and analyzed spectral estimators.
result A spectral estimate of interaction latent positions can achieve perfect clustering with enough interactions.
Generative model for hypergraph clustering improves detection of higher-order structure.
problem Detecting clusters in complex relational systems modeled as hypergraphs.
method Poisson degree-corrected hypergraph stochastic blockmodel (DCHSBM) and Louvain-type algorithms.
result AON hypergraph Louvain algorithm efficiently detects higher-order structure in large hypergraphs.
We propose a new method to model multi-way similarities into hypergraphs for clustering.
problem Clustering real-valued data using hypergraphs with multi-way similarities.
method Formulate multi-way similarities using kernel functions, establish connections to hypergraph cut, and develop a fast spectral clustering algorithm.
result Our method outperforms existing graph and heuristic modeling methods in clustering performance.
New algorithm improves hypergraph clustering for unbalanced communities.
problem Hypergraph clustering with unbalanced community sizes and outliers.
method CRTMLE algorithm using convex relaxation of truncated MLE.
result Achieves optimal recovery guarantees for unbalanced community sizes.
New method uses Ricci curvature for hypergraph clustering, outperforming existing techniques.
problem Community detection in hypergraphs with large hyperedges.
method Extending Ricci flow to hypergraphs by defining edge probability measures and transporting them on the line expansion.
result Enhanced sensitivity to hypergraph structure, especially in large hyperedges.
Hypergraph partitioning is an important problem in machine learning, computer vision and network analytics. A widely used method for hypergraph partitioning relies on minimizing a normalized sum of the costs of partitioning hyperedges across clusters. Algorithmic solutions based on this approach assume that different p…
Clustering on hypergraphs has been garnering increased attention with potential applications in network analysis, VLSI design and computer vision, among others. In this work, we generalize the framework of modularity maximization for clustering on hypergraphs. To this end, we introduce a hypergraph null model, analogou…
A new method clusters intersecting lines using hypergraphs.
problem Clustering intersecting lines in subspace clustering.
method Constructing a geometric hypergraph and using spectral algorithm.
result Achieves information-theoretic bounds for line clustering.
New hypergraph method improves scRNA-seq clustering.
problem Loss of higher-order information and overestimation in coexpression networks.
method Conceptualizing scRNA-seq data as hypergraphs and proposing novel clustering methods.
result Proposed methods outperform existing methods on simulated and real datasets.
The paper clusters hypergraphs to find diverse and experienced groups based on past experiences.
problem Finding diverse and experienced groups with respect to past experiences.
method Regularized edge-based hypergraph clustering objective with a 2-approximation algorithm.
result Demonstrates an efficient 2-approximation algorithm for clustering hypergraphs.
We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with k blocks of equal size. More precisely, we consider a random d-uniform hypergraph H with n vertices partitioned into k clusters of size s=n/k. Hyperedges e are added independently with probability p if e is…
Exact partitioning of high-order planted models achieved through convex optimization.
problem Efficiently partitioning hypergraphs generated by high-order planted models.
method Solving a computationally efficient convex optimization problem with a tensor nuclear norm constraint.
result Exact recovery of true underlying cluster structures with high probability.
HLRC offers a new curvature metric for hypergraphs that balances interpretability and efficiency.
problem Challenges in geometric characterization of hypergraphs with higher-order interactions.
method Hypergraph lower Ricci curvature (HLRC) defined in closed form.
result HLRC consistently reveals meaningful higher-order organization in diverse hypergraph datasets.
Modern graph or network datasets often contain rich structure that goes beyond simple pairwise connections between nodes. This calls for complex representations that can capture, for instance, edges of different types as well as so-called "higher-order interactions" that involve more than two nodes at a time. However, …
SDP approach recovers communities in multilayer hypergraphs from aggregated similarity matrices.
problem Community recovery in multilayer hypergraphs using aggregated similarity matrices.
method Semidefinite programming (SDP) approach.
result Information-theoretic conditions for exact recovery in both assortative and disassortative cases.
Community detection in hypergraphs is explored. Under a generative hypergraph model called "d-wise hypergraph stochastic block model" (d-hSBM) which naturally extends the Stochastic Block Model from graphs to d-uniform hypergraphs, the asymptotic minimax mismatch ratio is characterized. For proving the achievability, w…
In a series of recent works, we have generalised the consistency results in the stochastic block model literature to the case of uniform and non-uniform hypergraphs. The present paper continues the same line of study, where we focus on partitioning weighted uniform hypergraphs---a problem often encountered in computer …
Spectral clustering is a celebrated algorithm that partitions objects based on pairwise similarity information. While this approach has been successfully applied to a variety of domains, it comes with limitations. The reason is that there are many other applications in which only \emph{multi}-way similarity measures ar…
New method detects communities in complex hypergraphs, matching theoretical limits.
problem Detecting communities in non-uniform hypergraphs with varying hyperedge sizes.
method Developed a spectral theory for weighted non-backtracking operators on non-uniform hypergraphs.
result Achieved the Kesten-Stigum bound for weak recovery in a general class of non-uniform HSBMs.
New algorithm achieves strong consistency in binary non-uniform hypergraph classification.
problem Node classification on binary non-uniform hypergraphs with varying edge probabilities.
method Proposes a refinement algorithm using power iteration on weighted adjacency matrices.
result Proves optimality of the refinement algorithm, achieving strong consistency and IT lower bound.
Paper finds exact recovery threshold in general hypergraph model.
problem Exact recovery of communities in general hypergraph model.
method Developed a two-stage polynomial-time algorithm for exact recovery.
result Sharp threshold for exact recovery in terms of generalized Chernoff-Hellinger divergence.
Paper studies community detection in censored hypergraphs using information theory.
problem Community detection in censored hypergraphs with missing values.
method Information-theoretic approach, polynomial-time algorithm, spectral algorithm with refinement.
result Derives information-theoretic threshold for exact recovery of community structure.
Paper explores limits of high-order clustering with planted structures.
problem Statistical and computational limits of high-order clustering with planted structures.
method Developed methods for detection and recovery of clusters, identified signal-to-noise ratio boundaries.
result Sharp boundaries of signal-to-noise ratio for statistical and computational feasibility.
We present a hybrid method for latent information discovery on the data sets containing both text content and connection structure based on constrained low rank approximation. The new method jointly optimizes the Nonnegative Matrix Factorization (NMF) objective function for text clustering and the Symmetric NMF (SymNMF…
Proposes a tensor Laplacian-based method for better subspace clustering of non-uniformly distributed data.
problem LRR's inability to handle non-uniform data distribution and local information loss.
method Tensor Laplacian Regularized Low-Rank Representation (TLRR) using hypergraph model and tensor Laplacian algorithm.
result Higher accuracy and precision in subspace clustering compared to state-of-the-art methods.
Hypergraphs allow one to encode higher-order relationships in data and are thus a very flexible modeling tool. Current learning methods are either based on approximations of the hypergraphs via graphs or on tensor methods which are only applicable under special conditions. In this paper, we present a new learning frame…
Study compares hypergraph and graph-level models for higher-order relational learning.
problem Evaluating effectiveness of hypergraph-level vs. graph-level models in relational learning.
method Systematic evaluation of various hypergraph and graph-level architectures.
result Graph-level models applied to hypergraph expansions outperform hypergraph-level models.
Develops a Markov Random Field model for hypergraphs to improve machine learning tasks.
problem Modeling data generation processes on hypergraphs for better machine learning.
method Hypergraph Markov Random Field model using multivariate Gaussian distribution.
result Proposed model enhances algorithm design and outperforms existing methods in structure inference and node classification.
HyperBERT enhances BERT for node classification on text-attributed hypergraphs.
problem Challenges in capturing hypergraph structure and text attributes in node classification.
method Mixing hypergraph-aware layers with BERT for improved node classification.
result HyperBERT achieves state-of-the-art results on text-attributed hypergraph benchmarks.
A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.
problem Information loss in hypergraph expansions on either vertex or hyperedge level.
method Proposes a new hypergraph formulation named line expansion (LE) that treats vertices and hyperedges symmetrically.
result The proposed line expansion method outperforms state-of-the-art baselines on five hypergraph datasets.
Extends graph theory to hypergraphs with manifold-valued nodes.
problem Representing complex N-ary relationships on manifolds.
method Defined function spaces and symmetric products for manifold-valued nodes and edges.
result Generalized hypergraph Laplacians to manifold-valued hypergraphs.
The graph Laplacian plays key roles in information processing of relational data, and has analogies with the Laplacian in differential geometry. In this paper, we generalize the analogy between graph Laplacian and differential geometry to the hypergraph setting, and propose a novel hypergraph p-Laplacian. Unlike the …
Paper introduces a noise-robust classification method using hypergraph neural networks.
problem Noisy label learning problem in image datasets.
method PCA for dimensionality reduction, then applies graph-based semi-supervised learning methods including hypergraph neural network.
result Our proposed hypergraph neural network achieves the best performance when noise level increases.
New method detects communities in hypergraphs by embedding them into a vector space.
problem Detecting communities in hypergraphs with multi-way interactions.
method Augmenting non-uniform hypergraphs, embedding into a vector space, using an alternative updating scheme.
result Asymptotic consistencies in community detection and hypergraph estimation established.
Higher-order motif structures and multi-vertex interactions are becoming increasingly important in studies that aim to improve our understanding of functionalities and evolution patterns of networks. To elucidate the role of higher-order structures in community detection problems over complex networks, we introduce the…
Hypergraphs are used in machine learning to model higher-order relationships in data. While spectral methods for graphs are well-established, spectral theory for hypergraphs remains an active area of research. In this paper, we use random walks to develop a spectral theory for hypergraphs with edge-dependent vertex wei…
Recently, graph neural networks have attracted great attention and achieved prominent performance in various research fields. Most of those algorithms have assumed pairwise relationships of objects of interest. However, in many real applications, the relationships between objects are in higher-order, beyond a pairwise …
A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.
problem Capturing super-dyadic interactions in k-uniform hypergraphs.
method Tensor-based representation and tensor eigenvalue decomposition for capturing interactions.
result Improved min-cut solution on 2-uniform hypergraphs (graphs) compared to standard spectral partitioning.
Unified LLY Ricci curvature defined for hypergraphs.
problem Defining Ricci curvature for hypergraphs.
method Unified framework for LLY Ricci curvature on hypergraphs, establishing bounds and proving properties.
result Bonnet-Myers-type theorem for hypergraphs, highlighting curvature's potential in hypergraph analysis.
Paper learns hypergraph structures from signals with smoothness priors.
problem Learning hypergraph structures from signals with high-order relationships.
method Proposes HGSL framework with dual smoothness prior to map signals to hypergraph structure.
result HGSL efficiently infers meaningful hypergraph topologies from signals.
Develops neural network for directed hypergraphs for node classification.
problem Irregular data structure, particularly directed graphs.
method Directed hypergraph neural network and semi-supervised learning method.
result Novel directed hypergraph neural network achieves highest accuracies on node classification tasks.
In many real-world network datasets such as co-authorship, co-citation, email communication, etc., relationships are complex and go beyond pairwise. Hypergraphs provide a flexible and natural modeling tool to model such complex relationships. The obvious existence of such complex relationships in many real-world networ…
We consider the community detection problem in sparse random hypergraphs. Angelini et al. (2015) conjectured the existence of a sharp threshold on model parameters for community detection in sparse hypergraphs generated by a hypergraph stochastic block model. We solve the positive part of the conjecture for the case of…
Derives a Matern Gaussian process on hypergraphs for regression and embedding.
problem Regression and embedding of vertices in hypergraphs with uncertainty.
method Derives a Matern Gaussian process on hypergraphs, embeds vertices into latent space, identifies inducing vertices for scalable inference.
result Enables estimation of regression models with hypergraph structure informed correlation and uncertainty.
Study information limits for community detection in sub-hypergraphs.
problem Identify limits for exact community detection in sub-hypergraphs.
method Use Fano's inequality to define model parameters and identify success and failure regions.
result Identify regions where algorithms succeed or fail in exact recovery.
The study connects hypergraphs to strong homotopy Lie algebras.
problem Characterizing hypergraphs with a system of distinct representatives.
method Describing a procedure to attach nilpotent strong homotopy Lie algebras to hypergraphs.
result Isomorphic hypergraphs correspond to isomorphic strong homotopy Lie algebras.
HNHN learns from hypergraphs with hyperedge neurons for better classification.
problem Learning from hypergraphs with complex relationships.
method Hypergraph convolution network with hyperedge neurons and adaptive normalization.
result Improved classification accuracy and speed compared to state-of-the-art methods.