Heterogeneous Hypernetwork Representation Learning with Dual-End Weight Constraints

0
0
0

Heterogeneous Hypernetwork Representation Learning with Dual-End Weight Constraints

Introduction

Traditional networks have been widely studied in network representation learning, where nodes are mapped into low-dimensional vector spaces. However, these methods are not well-suited for hypernetworks, which possess complex higher-order tuple relationships. Unlike traditional networks that primarily capture pairwise relationships, hypernetworks involve interactions among multiple nodes through hyperedges, making their representation learning more challenging. Existing hypernetwork representation learning methods often struggle to effectively capture these higher-order relationships, leading to suboptimal performance in tasks such as link prediction and hypernetwork reconstruction.

To address these limitations, this paper proposes a novel method called Heterogeneous Hypernetwork Representation Learning with Dual-End Weight Constraints (HRDC). The key innovation of HRDC lies in its ability to integrate hyperedges into node sequences through a hyperedge multi-source random walk fusion algorithm and leverage a weighted fusion of hyperedge perceptron and hyper-gram models. This approach ensures that both pairwise relationships and higher-order tuple relationships are effectively captured, resulting in high-quality node embeddings.

Background and Related Work

Traditional Network Representation Learning

Traditional network representation learning methods, such as DeepWalk and node2vec, focus on capturing pairwise relationships between nodes. DeepWalk employs random walks to generate node sequences and applies the skip-gram model to learn node embeddings. Node2vec improves upon DeepWalk by introducing biased random walks that balance breadth-first and depth-first search strategies. However, these methods are not designed to handle the complex higher-order interactions present in hypernetworks.

Hypernetwork Representation Learning

Hypernetwork representation learning methods can be broadly categorized into spectral analysis-based and neural network-based approaches.

Spectral Analysis-Based Methods

Spectral analysis methods rely on matrix factorization techniques to derive node embeddings. These methods can be further divided into expansion-based and non-expansion-based approaches. Expansion-based methods, such as star expansion and clique expansion, convert hypernetworks into traditional networks before applying standard embedding techniques. While these methods simplify the problem, they often lose critical structural information inherent in hyperedges. Non-expansion-based methods, such as those using hypergraph Laplacian matrices, directly model hypernetworks but may fail when dealing with isolated nodes or weighted hyperedges.

Neural Network-Based Methods

Neural network-based approaches leverage deep learning architectures to capture hypernetwork structures. Expansion-based neural methods, such as Hypergraph Neural Networks (HGNN), apply graph convolutional networks to hypergraphs after transformation. However, these methods still suffer from information loss due to the expansion process. Non-expansion-based methods, such as Hyper-SAGNN and DHNE, avoid hyperedge decomposition and better preserve structural information. Hyper-SAGNN uses self-attention mechanisms to handle hyperedges of varying sizes, while DHNE employs multi-layer perceptrons to model higher-order relationships. Despite their strengths, these methods often face computational complexity or limited adaptability to diverse hypernetworks.

Problem Definition

A hypernetwork is typically represented as a hypergraph ( H = (V, E) ), where ( V ) is a set of nodes and ( E ) is a set of hyperedges. Each hyperedge ( e in E ) consists of multiple nodes, representing a higher-order relationship. Heterogeneous hypernetworks contain nodes of different types, further complicating the representation learning process.

The primary challenge in hypernetwork representation learning is to capture both pairwise relationships and higher-order tuple relationships without losing structural information. Existing methods either fail to adequately model hyperedges or suffer from high computational costs. HRDC addresses these challenges by introducing a dual-end weighting mechanism that balances the contributions of pairwise and higher-order relationships.

Methodology

Hyperedge Multi-Source Random Walk Fusion Algorithm

To better capture hypernetwork structures, HRDC introduces a hyperedge multi-source random walk fusion algorithm. This algorithm integrates hyperedges into node sequences generated by hyperpath-based random walks. The process involves three key steps:

  1. Computing Hyperedge Indecomposability: The algorithm first evaluates the indecomposability of hyperedges, which measures how tightly the nodes within a hyperedge are interconnected. This is done by analyzing whether subsets of hyperedges frequently appear in other hyperedges.
  2. Calculating Transition Probabilities: Based on the indecomposability scores, the algorithm computes transition probabilities for nodes during random walks. Nodes with higher indecomposability scores are more likely to be traversed, ensuring that critical higher-order relationships are preserved.
  3. Generating Node Sequences: The random walk process generates sequences where hyperedges are treated as nodes and inserted into the sequences. This ensures that both node interactions and hyperedge structures are captured in the embeddings.

Hyper-Gram Model

The hyper-gram model is inspired by the skip-gram model but extends it to handle both pairwise and higher-order relationships. It defines two similarity functions:

  1. Pairwise Similarity: This function measures the similarity between two nodes based on their co-occurrence in random walk sequences. It is optimized using negative sampling to improve computational efficiency.
  2. Tuple Similarity: This function evaluates the closeness of nodes within a hyperedge. A convolutional neural network is used to process node embeddings within a hyperedge, and a similarity score is computed to reflect the strength of the higher-order relationship.

The hyper-gram model combines these two functions into a unified objective function, ensuring that both types of relationships contribute to the final node embeddings.

Hyperedge Perceptron Model

Inspired by the TransE knowledge representation learning model, the hyperedge perceptron model treats hyperedges as nodes and learns embeddings by optimizing a translation-based objective function. The key idea is that the sum of a node embedding and a hyperedge embedding should approximate the embedding of another node connected by the same hyperedge. This approach effectively captures the semantic relationships between nodes and hyperedges.

Weighted Fusion Model

The final step in HRDC is the weighted fusion of embeddings generated by the hyper-gram and hyperedge perceptron models. The fusion is governed by balance factors ( alpha ) and ( beta ), which control the contribution of each model. The combined embeddings are computed as:

[ S_v = alpha cdot e_v + beta cdot f_v ]

where ( e_v ) is the embedding from the hyper-gram model, and ( f_v ) is the embedding from the hyperedge perceptron model. The balance factors are tuned to ensure optimal performance across different datasets.

Experiments

Datasets

HRDC was evaluated on four real-world hypernetwork datasets:

  1. GPS: Captures user-location-activity interactions.
  2. Drug: Records user-drug-reaction relationships.
  3. MovieLens: Represents user-movie-tag associations.
  4. WordNet: Contains head-relation-tail triples.

Baseline Methods

HRDC was compared against several baseline methods, including DeepWalk, node2vec, HPSG, HPHM, hyper2vec, CoarSAS2hvec, HyperS2V, HPHG, Hyper-SAGNN, and DHNE.

Link Prediction

Link prediction experiments were conducted to evaluate the ability of HRDC to predict future connections. The results demonstrated that HRDC outperformed most baseline methods across all datasets. Notably, HRDC achieved superior performance in capturing higher-order relationships, particularly in datasets with strong hyperedge structures like GPS and Drug.

Hypernetwork Reconstruction

Hypernetwork reconstruction experiments assessed how well HRDC preserved the original hypernetwork structure when reconstructing hyperedges. HRDC consistently performed well, especially in the GPS dataset, where it outperformed all baselines. In the Drug dataset, HRDC excelled when the hyperedge reconstruction ratio exceeded 0.3.

Parameter Sensitivity Analysis

The impact of balance factors ( alpha ) and ( beta ) was analyzed to determine their optimal values. The experiments revealed that the best performance was achieved when ( alpha ) was set to 0.9 and ( beta ) to 0.1 for the GPS dataset, and ( alpha = 1 ), ( beta = 0.1 ) for the Drug dataset. These settings ensured a balanced contribution from both models.

Ablation Study

Ablation studies confirmed the importance of both the hyper-gram and hyperedge perceptron models. Removing either component led to a decline in performance, highlighting the necessity of their combined use in HRDC.

Conclusion

HRDC represents a significant advancement in hypernetwork representation learning by effectively capturing both pairwise and higher-order relationships. The integration of hyperedges into random walk sequences and the weighted fusion of hyper-gram and hyperedge perceptron models ensure high-quality embeddings. Experimental results demonstrated HRDC’s superiority in link prediction and hypernetwork reconstruction tasks.

Future work will focus on optimizing the model to reduce redundancy in hypernetwork structure information and further improving computational efficiency.

doi.org/10.19734/j.issn.1001-3695.2024.07.0279

Was this helpful?

0 / 0