arXiv research

Develops a Markov Random Field model for hypergraphs to improve machine learning tasks.

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.

Paper introduces a noise-robust classification method using hypergraph neural networks.

A new hypergraph expansion method treats vertices and hyperedges equally, improving node classification.

Paper learns hypergraph structures from signals with smoothness priors.

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 …

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…

Develops neural network for directed hypergraphs for node classification.

HyperBERT enhances BERT for node classification on text-attributed hypergraphs.

New hypergraph neural network learns variable-sized hyperedges.

HyperSAGE learns node representations in hypergraphs without losing information.

HNHN learns from hypergraphs with hyperedge neurons for better classification.

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…

Two randomized algorithms improve hypergraph learning accuracy and efficiency.

Proposes a framework for deep learning on hypergraphs.

HYVINT generates hypergraphs with intensity-driven incidence formation and variational learning.

Study learns random hypergraphs with queries, improving on previous results.

Hyper-SAGNN learns patterns in hypergraphs for complex interactions.

New topological methods for hypergraph data improve community detection and pattern recognition.

Generative model for hypergraphs captures complex interactions without pairwise reductions.

We propose a hypergraph-based active learning scheme which we term $HS^2$, $HS^2$ generalizes the previously reported algorithm $S^2$ originally proposed for graph-based active learning with pointwise queries [Dasarathy et al., COLT 2015]. Our $HS^2$ method can accommodate hypergraph structures and allows one to ask bo…

Most network-based machine learning methods assume that the labels of two adjacent samples in the network are likely to be the same. However, assuming the pairwise relationship between samples is not complete. The information a group of samples that shows very similar pattern and tends to have similar labels is missed.…

A novel hypergraph partitioning method using tensor eigenvalue decomposition captures super-dyadic interactions.

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 …

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…

Inspired by recent interests of developing machine learning and data mining algorithms on hypergraphs, we investigate in this paper the semi-supervised learning algorithm of propagating "soft labels" (e.g. probability distributions, class membership scores) over hypergraphs, by means of optimal transportation. Borrowin…

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…

Improves hypergraph link prediction by breaking symmetry.

We introduce a new convex optimization problem, termed quadratic decomposable submodular function minimization (QDSFM), which allows to model a number of learning tasks on graphs and hypergraphs. The problem exhibits close ties to decomposable submodular function minimization (DSFM), yet is much more challenging to sol…

Extends graph theory to hypergraphs with manifold-valued nodes.

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 …

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…

Diffuse interface methods have recently been introduced for the task of semi-supervised learning. The underlying model is well-known in materials science but was extended to graphs using a Ginzburg--Landau functional and the graph Laplacian. We here generalize the previously proposed model by a non-smooth potential fun…

Self-supervised pretraining for heterogeneous hypergraphs improves graph-based tasks.

New method detects communities in hypergraphs by embedding them into a vector space.

Perfect clustering achieved in hypergraphs with enough interactions.

A training-free message passing module improves hypergraph neural networks.

FactorGCL uses hypergraph learning to predict stock returns by mining hidden factors.

Develops PageRank for directed hypergraphs using metabolic network.

Unified LLY Ricci curvature defined for hypergraphs.

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…

Biological and cellular systems are often modeled as graphs in which vertices represent objects of interest (genes, proteins, drugs) and edges represent relational ties among these objects (binds-to, interacts-with, regulates). This approach has been highly successful owing to the theory, methodology and software that …

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.

Study information limits for community detection in sub-hypergraphs.

A new GP framework for discovering unknown functions and hypergraph structure.