From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an effective, unified framework for using hyperedge and vertex embeddings jointly …
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48 results for “large hyperedges”
New hypergraph neural network learns variable-sized hyperedges.
problem Learning representations for non-uniform hypergraphs with variable cardinalities.
method Developed a hypergraph neural network exploiting incidence structure.
result Significant improvement in accuracy on real-world hypergraph datasets.
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.
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.
A framework infers hyperedges and overlapping communities in hypergraphs.
problem Characterizing the structural organization of hypergraphs with higher-order interactions.
method Statistical inference to infer missing hyperedges and detect overlapping communities.
result Efficient numerical implementation and strong performance on real-world systems.
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…
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.
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…
Paper tackles high-order inference in structured prediction tasks.
problem Maximizing a score function on the space of labels in high-order Markov random fields.
method Generative model approach with two-stage convex optimization algorithm.
result Success in general high-order inference problems driven by hyperedge expansion properties.
Improves hypergraph link prediction by breaking symmetry.
problem Limited expressivity of GWL-1 algorithm in hypergraph link prediction.
method Preprocessing algorithm to identify and replace symmetry-inducing subhypergraphs with covering hyperedges.
result Improves expressivity of GWL-1, leading to better link prediction.
Bayesian hypergraph inference models disease pathways from EHR data.
problem Modeling rare diseases influenced by shared risk factors.
method Bayesian hypergraph inference framework reframing multi-disease modeling.
result Interpretable disease pathways and well-calibrated uncertainty quantification.
Study learns random hypergraphs with queries, improving on previous results.
problem Learn random hypergraphs with non-adaptive queries.
method Equivalence to group testing, using Erdős-Rényi model for graphs.
result Generalization to random -uniform hypergraphs.
Paper proposes HGTAN for better stock trend prediction.
problem Predicting stock price trends is challenging and crucial for investors.
method Temporal-relational hypergraph tri-attention network (HGTAN).
result HGTAN outperforms existing methods in stock trend prediction.
Spectral algorithm recovers community structure in sparse hypergraphs.
problem Community detection in sparse random hypergraphs with community structure and higher-order interactions.
method Spectral algorithm with three steps: hyperedge selection, spectral partition, and correction/merging.
result Weak consistency achieved for weak signal-to-noise ratio.
We consider the exact recovery problem in the hypergraph stochastic block model (HSBM) with blocks of equal size. More precisely, we consider a random -uniform hypergraph with vertices partitioned into clusters of size . Hyperedges are added independently with probability if is…
We investigate probabilistic graphical models that allow for both cycles and latent variables. For this we introduce directed graphs with hyperedges (HEDGes), generalizing and combining both marginalized directed acyclic graphs (mDAGs) that can model latent (dependent) variables, and directed mixed graphs (DMGs) that c…
Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various lea…
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…
In this paper, we present a hypergraph neural networks (HGNN) framework for data representation learning, which can encode high-order data correlation in a hypergraph structure. Confronting the challenges of learning representation for complex data in real practice, we propose to incorporate such data structure in a hy…
New tensor framework connects Fisher information, hypergraphs, and multi-observable correlations.
problem Missing structure in pairwise Fisher graphs for multi-observable radiation patterns.
method Higher-order Fisher tensors and natural exponential-family coordinates.
result Exact triality of Fisher tensors, cumulants, and hypergraphs.
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.
Community detection in graphs has been extensively studied both in theory and in applications. However, detecting communities in hypergraphs is more challenging. In this paper, we propose a tensor decomposition approach for guaranteed learning of communities in a special class of hypergraphs modeling social tagging sys…
HyperSAGE learns node representations in hypergraphs without losing information.
problem Learning node representations in hypergraphs is complex due to higher-order relations.
method Two-level neural message passing strategy for accurate information propagation.
result HyperSAGE outperforms state-of-the-art methods on benchmark datasets.
New method combines hypergraph structure and node attributes for better community detection.
problem Improving community detection in hypergraphs with node attributes.
method Developed a principled model that learns from data to combine higher-order interactions and node attributes.
result Strong performance in hyperedge prediction and community detection, especially when attributes are informative.
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.
Wavelets model complex interactions in spatial transcriptomics.
problem Capturing higher-order relationships in spatial transcriptomics data.
method Hypergraph diffusion wavelets for representing hyperedges.
result Wavelets effectively represent disease-relevant cellular niches in Alzheimer's disease.
A new algorithm reduces frequentist regret in multi-agent bandit problems with sparse hypergraphs.
problem Deriving a frequentist regret bound for Thompson sampling in multi-agent settings with sparse hypergraphs.
method Proposed -exploring Multi-Agent Thompson Sampling (-MATS) algorithm that combines exploration and exploitation strategies.
result Achieves a worst-case frequentist regret bound sublinear in time horizon and local arm size, optimal up to constants and logarithms for sparse hypergraphs.
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.
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.
A quantum framework optimizes collateral allocation for derivatives.
problem Legal constraints and operational rules in collateral allocation for derivatives.
method Certified higher-order quantum framework that normalizes margin requirements and builds a bounded neighborhood of actions.
result Quantum framework improves certified sample quality compared to classical methods.
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…
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.
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.
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.
The goal of unsupervised representation learning is to extract a new representation of data, such that solving many different tasks becomes easier. Existing methods typically focus on vectorized data and offer little support for relational data, which additionally describe relationships among instances. In this work we…
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.
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.
HYVINT generates hypergraphs with intensity-driven incidence formation and variational learning.
problem Challenges in generating hypergraphs with mechanistic interpretation and limited latent space.
method HYVINT uses intensity-driven incidence formation and a lower-bound variational estimator for latent representations.
result HYVINT achieves strong fidelity and novelty on synthetic and real-world hypergraphs.
Structure of international trade hypergraphsphysics.soc-ph
Study the structure of international trade through hypergraphs.
problem Understanding the complex relationships in international trade networks.
method Analyzing the mean hyperdegree of adjacent vertices and decomposing correlation properties.
result Identifies bias in trade relationships not visible in pairwise networks.
Hypergraph is a general way of representing high-order relations on a set of objects. It is a generalization of graph, in which only pairwise relations can be represented. It finds applications in various domains where relationships of more than two objects are observed. On a hypergraph, as a generalization of graph, o…
Generative model for hypergraphs captures complex interactions without pairwise reductions.
problem Challenges in generating realistic hypergraphs with pairwise reductions.
method Structured stochastic diffusion on relaxed incidence matrices.
result Generative model preserves structure-aware noising and yields explicit Gaussian law.
CSHT predicts financial returns from news using a novel transformer model on a sphere.
problem Financial forecasting from news and sentiment.
method Granger-causal hypergraph structure, Riemannian geometry, causally masked Transformer attention.
result CSHT outperforms baselines in return prediction, regime classification, and asset ranking.
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.
In various application areas, networked data is collected by measuring interactions involving some specific set of core nodes. This results in a network dataset containing the core nodes along with a potentially much larger set of fringe nodes that all have at least one interaction with a core node. In many settings, t…
Sharp threshold for exact recovery in non-uniform hypergraph stochastic block model.
problem Community detection in random hypergraphs with non-uniform hyperedge probabilities.
method Sharp threshold established; two efficient algorithms for exact recovery.
result Sharp threshold for exact recovery; information-theoretic lower bound on misclassification.
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.
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.
Proposes PEID for analyzing synergistic causation in complex systems.
problem Challenges in identifying and analyzing synergistic causation in complex systems.
method Partial Effective Information Decomposition (PEID) framework.
result Unified and computable characterization of synergistic causal relations.