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…
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48 results for “Hypergraph Stochastic Block Model”
Information Theoretic Limits of Exact Recovery in Sub-hypergraph Models for Community Detectionstat.ML
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.
Hypergraph partitioning lies at the heart of a number of problems in machine learning and network sciences. Many algorithms for hypergraph partitioning have been proposed that extend standard approaches for graph partitioning to the case of hypergraphs. However, theoretical aspects of such methods have seldom received …
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.
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.
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 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.
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.
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…
Spectral method detects communities in sparse hypergraphs, achieving detection threshold.
problem Community detection in sparse hypergraphs.
method Non-backtracking operator and spectral approach.
result Spectral method achieves detection threshold for sparse 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.
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…
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.
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 …
The high-order relations between the content in social media sharing platforms are frequently modeled by a hypergraph. Either hypergraph Laplacian matrix or the adjacency matrix is a big matrix. Randomized algorithms are used for low-rank factorizations in order to approximately decompose and eventually invert such big…
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…
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.
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…
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.
Tutorials on signal processing on higher-order networks like simplicial complexes and hypergraphs.
problem Processing complex data structures with polyadic relationships.
method Introduction to simplicial complexes and hypergraphs, Fourier analysis, signal denoising, interpolation, embeddings, neural networks.
result Multi-relational operators like the Hodge Laplacian for simplicial complexes and tensor representations for hypergraphs.
Low coordinate degree algorithms II: Categorical signals and generalized stochastic block modelsmath.ST
New algorithms detect categorical structures in high-dimensional data.
problem Detecting categorical structures in high-dimensional data.
method Low coordinate degree functions (LCDF) applied to categorical and stochastic block models.
result Unified analysis of LCDF performance for various SBMs and tight lower bounds.
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.
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.
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.
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.
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…
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.
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…
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 …
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…
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.
THRML uses energy-based models for index tracking, reducing portfolio tracking error and improving returns.
problem NP-hard combinatorial optimization in portfolio optimization under cardinality constraints.
method THRML reformulates index tracking as probabilistic inference on an Ising Hamiltonian, using GPU-accelerated block Gibbs sampling.
result THRML achieves 4.31 percent annualized tracking error compared to 5.66-6.30 percent for baselines, with 128.63 percent total return.
During the last two decades, we easilly see that the World Wide Web's link structure is modeled as the directed graph. In this paper, we will model the World Wide Web's link structure as the directed hypergraph. Moreover, we will develop the PageRank algorithm for this directed hypergraph. Due to the lack of the World …
The paper sets thresholds for testing correlation in hypergraphs, distinguishing between independent and correlated states.
problem Testing correlation between two hypergraphs under different models.
method Derives sharp information-theoretic thresholds for distinguishing between null and alternative hypotheses.
result The testing threshold decreases as the hypergraph's uniformity (m) increases, making correlation testing easier for higher uniformity.
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 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.
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.
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.
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 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.
A central problem in analyzing networks is partitioning them into modules or communities. One of the best tools for this is the stochastic block model, which clusters vertices into blocks with statistically homogeneous pattern of links. Despite its flexibility and popularity, there has been a lack of principled statist…
Paper introduces models to discover complex structures in large hypergraphs.
problem Understanding dependency structures in complex systems represented as hypergraphs.
method Probabilistic models treating classes of similar units as nodes in a latent hypergraph, using low-rank representations.
result Improves link prediction and discovers interpretable structures in diverse real-world systems.
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 -Laplacian. Unlike the …
New topological methods for hypergraph data improve community detection and pattern recognition.
problem Community detection and pattern recognition in hypergraph data.
method Introducing a new topological space structure of hypergraph data, proposing modified nearest neighbors methods.
result Improved methods for community detection and pattern recognition in hypergraph 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.
We generalize the stochastic block model to the important case in which edges are annotated with weights drawn from an exponential family distribution. This generalization introduces several technical difficulties for model estimation, which we solve using a Bayesian approach. We introduce a variational algorithm that …