Paper proves consistency of spectral hypergraph partitioning under a new model.
problem Consistency of spectral hypergraph partitioning under a new model.
method Spectral hypergraph partitioning algorithm using matrix concentration inequalities.
result First consistency result for partitioning non-uniform hypergraphs.
New algorithms for efficient hypergraph partitioning in computer vision.
problem Efficiently partitioning weighted uniform hypergraphs for computer vision tasks.
method Provable tensor methods and sampling techniques.
result Rigorous analysis justifies practical sampling techniques.
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.
New hypergraph clustering method assigns different costs to hyperedge cuts.
problem Hypergraph partitioning assumes uniform costs for different hyperedge cuts.
method Inhomogeneous hypergraph partitioning assigns different costs to different hyperedge cuts.
result Inhomogeneous partitioning offers significant performance improvements in various applications.
Solves community detection in sparse hypergraphs above a threshold.
problem Community detection in sparse hypergraphs.
method Generalization of Massoulié's method for sparse random graphs to random hypergraphs.
result Above the threshold, a spectral algorithm constructs a partition correlated with the true partition.
New study shows limits of low-degree algorithms in finding large independent sets in sparse hypergraphs.
problem Finding large independent sets in sparse random hypergraphs.
method Low-degree polynomial algorithms are analyzed to determine their limits.
result Low-degree algorithms can find independent sets of density up to \(\left(\frac{\log d}{(r-1)d}
ight)^{1/(r-1)}\), but no larger.
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.
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.
Develops algorithms for multi-way similarity clustering in hypergraphs.
problem Challenges of spectral clustering in multi-way similarity settings.
method Hypergraph Spectral Clustering (HSC) and Hypergraph Spectral Clustering with Local Refinement (HSCLR).
result Achieves optimal performance under the weighted stochastic block model.
A new binary classification algorithm using hypergraphs reduces preprocessing needs.
problem Binary classification in unstructured spaces with missing data.
method Hypergraph representation, seminorm learning, partitioning elements based on training set interactions.
result Empirical validation shows high performance on various 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.
New optimization problem for graph and hypergraph learning tasks.
problem Learning tasks on graphs and hypergraphs.
method Quadratic decomposable submodular function minimization (QDSFM) via dual strategy and double-loop algorithms.
result Linear convergence rates for outer-loop optimization and effective hypergraph-based PageRank algorithm.
New invariant classifies right-angled Coxeter groups, bounds thickness.
problem Classifying and bounding right-angled Coxeter groups.
method Introducing hypergraph index from defining graph, computing upper bounds.
result Hypergraph index partitions groups into quasi-isometry classes, bounds thickness.
Deterministic tensor completion using hypergraph expanders with linear sample complexity.
problem Low-rank tensor recovery with minimal samples.
method Minimizing max-quasinorm of tensors using hypergraph expanders.
result Deterministic analysis shows linear sample complexity for tensor recovery.
Spectral algorithm recovers clusters in hypergraph with high probability.
problem Exact recovery of clusters in hypergraph stochastic block model.
method Spectral algorithm based on adjacency matrix of hypergraph.
result Exact recovery with high probability for k = Θ ( n ) k=Θ(\sqrt{n}) k = Θ ( n ) clusters. 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.
Unified framework for higher-order network analysis.
problem Complex structure of space of networks.
method Measure-theoretic formalism, Gromov-Wasserstein distance, co-optimal transport distance.
result Unified theoretical treatment of generalized networks.
Paper generalizes graph Laplacian to hypergraphs for semi-supervised learning.
problem Analyzing hypergraphs with edges connecting multiple nodes.
method Proposes hypergraph p p p -Laplacian and semi-supervised learning method. result Hypergraph p p p -Laplacian outperforms standard hypergraph Laplacians. Extends Borsuk-Ulam theorem with applications in sphere coverings and colorings.
problem Complexity bounds and structural insights for triangulated sphere mappings.
method Combinatorial labeling and order type analysis of finite point sets.
result New topological Hall theorem and generalizations of hypergraph Hall theorems.
New hypergraph operators improve graph neural networks for higher-order relationships.
problem Learning deep embeddings on high-order graph-structured data.
method Introducing hypergraph convolution and hypergraph attention operators.
result Extensive experimental results show the effectiveness of hypergraph operators.
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.
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…
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 paper develops a spectral theory for hypergraphs with edge-dependent vertex weights using random walks.
problem Lack of spectral theory for hypergraphs with edge-dependent vertex weights.
method Random walks on hypergraphs with edge-dependent vertex weights, deriving a random walk-based hypergraph Laplacian.
result Random walks on hypergraphs with edge-dependent vertex weights can capture higher-order relationships in data.
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.
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.
HyperGCN applies graph convolutional networks to hypergraphs for complex network learning.
problem Learning with complex relationships in hypergraphs.
method Proposes HyperGCN, a novel GCN for hypergraph semi-supervised learning.
result Demonstrates HyperGCN's effectiveness on real-world hypergraphs.
Develops PageRank for directed hypergraphs using metabolic network.
problem Lack of directed hypergraph datasets for PageRank algorithm.
method Developed PageRank algorithm for directed hypergraphs and applied it to metabolic network.
result Successfully applied novel PageRank algorithm to metabolic network.
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.
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.
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.
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.
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 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.
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.
Two randomized algorithms improve hypergraph learning accuracy and efficiency.
problem Efficiently learning and tagging images in hypergraphs.
method Block randomized SVD and conjugate gradient method.
result Both methods achieve high accuracy and reduce computational requirements.
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.
New curvature measure for hypergraphs using optimal transport.
problem Defining curvature for hypergraphs.
method Multi-marginal optimal transport for a random walk on hypergraphs.
result Coarse scalar curvature generalizes Ricci curvature for Markov chains.
Study evaluates methods for expanding communities in hypergraphs using random walks.
problem Expanding communities in hypergraphs using random walks.
method Clique-expansion and tensor methods evaluated; hybrid method proposed.
result Parameter regimes identified where methods outperform each other.
Unified curvature for hypergraphs from Ollivier-Ricci.
problem Generalizing curvature to hypergraphs.
method Developed ORCHID framework to generalize Ollivier-Ricci curvature to hypergraphs.
result ORCHID curvatures have favorable theoretical properties and are scalable for hypergraph tasks.