Dynamic Hypergraph Wavelet Neural Network for Semi-Supervised Hypergraph Node Classification

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Dynamic Hypergraph Wavelet Neural Network for Semi-Supervised Hypergraph Node Classification

Introduction

Graph-structured data, consisting of nodes and edges, is widely used to represent relationships in various domains such as social networks, knowledge graphs, and molecular structures. Semi-supervised node classification aims to predict the labels of unlabeled nodes using limited labeled data, enabling models to assign nodes to their correct categories. This task has broad applications, including social media analysis, recommendation systems, bioinformatics, and computer vision.

Traditional semi-supervised node classification methods primarily focus on ordinary graphs, where relationships are pairwise. Graph Neural Networks (GNNs) have been widely adopted for processing non-Euclidean data in such tasks. For instance, Graph Convolutional Networks (GCNs) leverage spectral theory to perform node classification, while Graph Attention Networks (GAT) use attention mechanisms to weigh neighbor contributions. However, these methods are designed for pairwise relationships and struggle with higher-order interactions, which are common in real-world scenarios.

Hypergraphs provide a natural way to model higher-order relationships, where hyperedges can connect multiple nodes simultaneously. For example, in a co-authorship network, a hyperedge can represent a group of authors collaborating on a paper, capturing interactions beyond pairwise connections. Despite their advantages, existing hypergraph-based methods face two key challenges:

  1. Hidden Higher-Order Relations: As neural network depth increases, static hypergraph structures fail to capture evolving node relationships.
  2. High Computational Complexity: Conventional hypergraph convolution operations involve extensive matrix decomposition and Fourier transforms, leading to inefficiency.

To address these limitations, this paper introduces the Dynamic Hypergraph Wavelet Neural Network (DHGWNN), a novel framework for semi-supervised hypergraph node classification. The key contributions include:
• A dynamic hypergraph construction method that iteratively refines hypergraph structures using k-NN, k-Hop, and attention mechanisms to uncover hidden higher-order relationships.

• A hypergraph wavelet convolutional network that replaces traditional Fourier-based convolutions with wavelet transforms, significantly reducing computational overhead.

Experiments on four citation network datasets demonstrate that DHGWNN outperforms existing baselines in classification accuracy while being computationally efficient.

Background and Related Work

Semi-Supervised Node Classification on Ordinary Graphs

Early approaches like DeepWalk and node2vec focused on capturing node proximity through random walks. More recently, GNN-based methods have dominated the field, falling into two categories:

  1. Spectral Methods: These approaches define convolution in the spectral domain using graph Fourier transforms. While theoretically sound, they suffer from high computational costs due to Laplacian matrix decomposition.
  2. Spatial Methods: These methods aggregate neighbor features using sampling and attention mechanisms. GraphSAGE samples fixed-size neighborhoods, while GAT dynamically weights neighbors based on importance.

Despite their success, these methods are limited to pairwise relationships and cannot naturally handle higher-order interactions.

Semi-Supervised Node Classification on Hypergraphs

Hypergraph-based methods can be categorized into:

  1. Spectral Methods: Early work by Zhou et al. extended graph Laplacians to hypergraphs, while Agarwal et al. proposed star and clique expansions to convert hypergraphs into ordinary graphs. However, these expansions often lead to information loss or redundancy.
  2. Neural Network Methods: Feng et al. introduced Hypergraph Neural Networks (HGNN), applying convolutional operations to hypergraphs. Subsequent improvements include HyperGCN, which uses sampling to reduce noise, and Hyper-Atten, which incorporates attention mechanisms. Recent work like DHGNN dynamically adjusts hypergraph structures during training, while HGNN+ extends convolutions to the spatial domain.

While these methods have advanced the field, they still suffer from:
• Static hypergraph structures that ignore evolving node relationships.

• High computational costs due to inefficient convolution operations.

Methodology

Problem Definition

A hypergraph is defined as ( mathcal{G} = (mathcal{V}, mathcal{E}, W) ), where ( mathcal{V} ) is a set of nodes, ( mathcal{E} ) is a set of hyperedges, and ( W ) is a diagonal matrix of hyperedge weights. The goal of semi-supervised hypergraph node classification is to learn a function ( f: mathcal{V} rightarrow C ) that maps nodes to their correct labels using limited labeled data.

Dynamic Hypergraph Construction

To capture hidden higher-order relationships, DHGWNN dynamically reconstructs the hypergraph at each neural network layer using:

  1. k-Nearest Neighbors (k-NN): Selects the top-k most relevant neighbors for each node based on attention weights, ensuring local connectivity.
  2. k-Hop Neighborhoods: Aggregates all nodes within k hops of a target node, providing global structural information.

These strategies are combined via concatenation to form a new hypergraph structure, which is fed into the next layer. This iterative process allows the model to adapt to evolving node features and uncover deeper relationships.

Hypergraph Wavelet Convolutional Network

Traditional hypergraph convolutions rely on Fourier transforms, which are computationally expensive. DHGWNN replaces these with wavelet transforms, offering two advantages:

  1. Sparsity: Wavelets provide localized frequency information, enabling efficient computation.
  2. Fast Algorithms: Wavelet transforms avoid matrix decomposition, reducing time complexity.

The wavelet-based convolution operation updates node features by propagating information through “node-hyperedge-node” transformations, refining node embeddings at each layer.

Attention Mechanism

To enhance feature aggregation, DHGWNN employs an attention mechanism that:

  1. Computes attention weights for nodes within a 2-hop neighborhood.
  2. Uses these weights to perform weighted feature aggregation, emphasizing more relevant neighbors.

This process improves the model’s ability to capture node similarities and dissimilarities.

Training Process

The training procedure involves:

  1. Initialization: Constructing an initial hypergraph from the input data.

  2. Iterative Refinement:
    • Applying wavelet convolutions to update node features.

    • Computing attention weights and aggregating features.

    • Reconstructing the hypergraph using k-NN and k-Hop.

  3. Classification: Training a classifier on the final node embeddings to predict labels.

The model optimizes a cross-entropy loss function to minimize prediction errors.

Experiments

Datasets

Experiments were conducted on four citation network datasets:
• Cora: 2,708 nodes, 5,429 edges, 7 classes.

• PubMed: 19,717 nodes, 44,338 edges, 3 classes.

• Citeseer: 3,327 nodes, 4,732 edges, 6 classes.

• DBLP: 41,302 nodes, 22,363 edges, 6 classes.

Baseline Models

DHGWNN was compared against:

  1. Ordinary Graph Methods: GCN, GraphSAGE, GAT, SC-HGANN.
  2. Hypergraph Methods: HyperGCN, Hyper-Atten, HGNN, HCNH, HGTN, HGNN+.

Results

  1. Classification Accuracy: DHGWNN achieved the highest accuracy on all datasets, outperforming the best baselines by 2.71% (Cora), 2.04% (PubMed), 1.59% (Citeseer), and 2.58% (DBLP).
  2. F1 Scores: Both macro-F1 and micro-F1 scores were higher than HGNN, demonstrating better performance in imbalanced class scenarios.
  3. Training Time: DHGWNN trained faster than DHGNN (a variant with traditional convolutions), validating the efficiency of wavelet transforms.

Ablation Studies

Removing either the dynamic hypergraph module or the wavelet convolutions degraded performance, confirming their complementary roles.

Parameter Analysis

Increasing network depth initially improved accuracy but led to declines beyond a certain point due to overfitting, suggesting an optimal depth of 2-3 layers.

Case Study

In the Cora dataset, DHGWNN correctly classified papers where baselines failed, particularly in cases requiring higher-order relationship reasoning.

Conclusion

DHGWNN advances semi-supervised hypergraph node classification by:

  1. Dynamically constructing hypergraphs to uncover hidden relationships.
  2. Leveraging wavelet transforms for efficient and effective convolutions.

Future work will focus on optimizing attention mechanisms to further reduce computational costs while maintaining performance.

doi.org/10.19734/j.issn.1001-3695.2024.05.0129

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