Source-linked AI summary
Hypergraph Neural Networks
Yifan Feng, Haoxuan You, Zizhao Zhang, Rongrong Ji, Yue Gao
TL;DR
Complex and multi-modal data may contain high-order correlations that pairwise graph models cannot adequately represent. The paper proposes HGNN, which combines hypergraph modeling with hyperedge convolution for representation learning, and reports better performance across citation classification and visual recognition tasks, especially for multi-modal data.
Problem
Complex and multi-modal data contain correlations beyond pairwise relationships, creating a need for more general data-structure models for representation learning.
Method
HGNN models complex correlations with hypergraphs and uses hyperedge convolution to learn representations from high-order data structure.
Results
HGNN outperforms graph convolutional and traditional methods across citation network classification and visual object recognition experiments, with stronger performance for multi-modal data.
Takeaways & Limitations
HGNN provides a general representation-learning framework that incorporates high-order, complex, and multi-modal correlations, while graph convolution is a special case.
Abstract
from arXiv · showhide
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 hypergraph, which is more flexible on data modeling, especially when dealing with complex data. In this method, a hyperedge convolution operation is designed to handle the data correlation during representation learning. In this way, traditional hypergraph learning procedure can be conducted using hyperedge convolution operations efficiently. HGNN is able to learn the hidden layer representation considering the high-order data structure, which is a general framework considering the complex data correlations. We have conducted experiments on citation network classification and visual object recognition tasks and compared HGNN with graph convolutional networks and other traditional methods. Experimental results demonstrate that the proposed HGNN method outperforms recent state-of-the-art methods. We can also reveal from the results that the proposed HGNN is superior when dealing with multi-modal data compared with existing methods.
Introduction
Traditional graph convolution models pairwise relationships, but complex and multi-modal data require richer correlation structures. HGNN addresses this with hypergraph modeling and hyperedge convolution, and reports stronger performance across evaluated tasks.
- Motivation: Real-world and multi-modal data can exhibit correlations beyond pairwise connections, limiting traditional graph-based modeling.Social-media examples include visual, text, and social connections among data points.
- Proposed framework: HGNN uses flexible, degree-free hyperedges to encode high-order, multi-modal, and heterogeneous data correlations.Unlike graph edges, which connect exactly two vertices, hyperedges can represent higher-order relationships.
- Proposed framework: The framework introduces hyperedge convolution to exploit complex correlations during representation learning.HGNN formulates data correlations with a hypergraph and uses convolution operations for learning representations.
- Evaluation: Experiments on citation network classification and visual object recognition show better HGNN performance than graph convolutional and traditional methods.The study evaluates four datasets and reports particular effectiveness for multi-modal data.
- Proposed framework: HGNN treats traditional graph convolutional networks as a special case in which graph edges are 2-order hyperedges.This places graph convolution within the broader hypergraph neural-network framework.
Related Work
Prior work developed hypergraph learning for high-order data correlation and graph neural networks for irregular structures. Graph convolution research spans spectral and spatial approaches, while the paper situates HGNN within these lines of work.
- Hypergraph learning: Earlier hypergraph-learning methods modeled high-order correlations and supported tasks such as propagation and video object segmentation.Hypergraph learning was introduced as propagation on a hypergraph and later applied to video object segmentation.
- Neural networks on graphs: Graph neural networks extended neural-network methods to irregular, non-grid data represented as graphs.The related work describes early recurrent graph networks and subsequent graph-convolution approaches.
- Neural networks on graphs: Spectral graph-convolution methods define convolution in the graph spectral domain using Laplacian eigenbases or polynomial approximations.The cited approaches include Fourier-like graph bases, smooth spectral filters, and Chebyshev expansions.
- Neural networks on graphs: Spatial graph-convolution methods define operations over spatially close neighborhoods using transition matrices, local path operators, or attention.The reviewed methods represent neighborhoods through powers of transition matrices, Gaussian-mixture path operators, or attention mechanisms.
Hypergraph Neural Networks
HGNN extends graph convolution to hypergraphs, representing high-order and multimodal correlations through efficient hyperedge convolution. Its node-edge-node transformation supports feature extraction while retaining graph convolution as a special case.
- Hypergraph representation: HGNN represents data with hypergraphs whose hyperedges connect two or more vertices, enabling high-order and multimodal correlation modeling.Unlike simple graphs, hypergraphs are not restricted to pairwise connections and can flexibly combine heterogeneous feature relationships.
- Hypergraph learning: Hypergraph learning formulates node classification as a regularization problem in which labels should be smooth over the hypergraph structure.The hypergraph Laplacian is positive semi-definite and defines the normalized regularizer used in the formulation.
- Spectral convolution: Spectral hypergraph convolution uses Fourier-domain filters, while truncated Chebyshev polynomials remove explicit eigenvector computation and reduce computation complexity.The method further sets K = 1 because the hypergraph Laplacian already represents high-order node correlation.
- Hyperedge convolution: The HGNN layer performs a normalized node-edge-node transform: filtering node features, aggregating them into hyperedge features, then returning aggregated node features.The incidence matrix H and degree matrices Dv and De implement hyperedge gathering, node aggregation, and normalization.
- Relations and applications: HGNN is computationally more efficient than traditional hypergraph methods, naturally models high-order relationships, and can expand to multimodal feature construction.When every hyperedge connects two vertices, the hypergraph reduces to a simple graph, making graph convolution a special case of HGNN.
Experiments
HGNN was evaluated on citation-network and visual-object classification, with comparisons against GCN and other state-of-the-art methods. Results show modest citation gains and stronger advantages for visual recognition, especially with multimodal features.
- Experiments covered citation network classification and visual object recognition, comparing HGNN with graph convolutional networks and other state-of-the-art methods.The citation datasets were Cora and Pubmed; visual datasets included ModelNet40 and NTU.
- Citation network classification: Compared with GCN, HGNN improved slightly on Cora and by 1.1% on Pubmed, where the generated hypergraph closely resembled the graph.The paper attributes the limited gain to the absence of additional or more complex relationship information in the citation data.
- Visual object classification: HGNN outperformed PointCNN and SO-Net on ModelNet40 by 4.8% and 3.2%, respectively.These comparisons were reported against recent object-recognition methods using two features.
- Visual object classification: HGNN outperformed GCN across visual experiments, with gains of 0.3% on ModelNet40 and 2.0% on NTU in a single-feature comparison.
- Visual object classification: On NTU, HGNN gained 8.3%, 10.4%, and 8.1% over GCN using GVCNN, MVCNN, and GVCNN+MVCNN object features, respectively.The paper links stronger performance to hypergraphs encoding high-order correlations and flexibly combining multimodal information.
Conclusion
HGNN generalizes convolution to hypergraph learning, enabling representation learning over complex and high-order correlations. Experiments on citation classification and visual object recognition show better performance than state-of-the-art methods, with potential applications in visual recognition, retrieval, and classification.
- HGNN generalizes convolution to hypergraph learning using a hypergraph Laplacian and truncated Chebyshev polynomial approximation.This supports handling complex and high-order correlations through hypergraph structure.
- HGNN evaluates complex-correlation representation learning on citation network classification and visual object recognition tasks.
- HGNN demonstrates better performance than state-of-the-art methods in the reported experiments.
- HGNN supports potential applications in visual recognition, retrieval, and data classification.