Hyper-SAGNN: a self-attention based graph neural network for hypergraphs (1911.02613v1)

Abstract: Graph representation learning for hypergraphs can be used to extract patterns among higher-order interactions that are critically important in many real world problems. Current approaches designed for hypergraphs, however, are unable to handle different types of hypergraphs and are typically not generic for various learning tasks. Indeed, models that can predict variable-sized heterogeneous hyperedges have not been available. Here we develop a new self-attention based graph neural network called Hyper-SAGNN applicable to homogeneous and heterogeneous hypergraphs with variable hyperedge sizes. We perform extensive evaluations on multiple datasets, including four benchmark network datasets and two single-cell Hi-C datasets in genomics. We demonstrate that Hyper-SAGNN significantly outperforms the state-of-the-art methods on traditional tasks while also achieving great performance on a new task called outsider identification. Hyper-SAGNN will be useful for graph representation learning to uncover complex higher-order interactions in different applications.

• The paper introduces Hyper-SAGNN, which uses self-attention to capture high-order interactions in hypergraphs and overcomes fixed-size limitations of previous models.
• It transforms node features into dynamic and static embeddings, enabling accurate hyperedge prediction and flexible integration of variable hyperedge sizes.
• Evaluation shows Hyper-SAGNN outperforms models like DHNE in hyperedge prediction, proving its effectiveness for complex structures in domains such as genomics.

Hyper-SAGNN: A Self-Attention Based Graph Neural Network for Hypergraphs

The paper presents a novel approach in the field of graph neural networks, specifically targeted at hypergraph structures, through the formulation of a model named Hyper-SAGNN (self-attention-based graph neural network). While traditional graph neural networks have demonstrated efficiency in various tasks such as link prediction and node classification, their application is predominantly restricted to pairwise interactions. This limitation presents a gap when dealing with hypergraphs, which are capable of representing higher-order interactions critical in numerous real-world scenarios.

Overview of Hyper-SAGNN

Hyper-SAGNN is designed to operate on both homogeneous and heterogeneous hypergraphs with variable hyperedge sizes, overcoming the limitations of previous models like DHNE, which could only manage fixed-size hyperedges and did not generalize well across different types of hyperedges. The model employs a self-attention mechanism, which is instrumental in addressing the varied and complex nature of hypergraphs, enabling the learning of embeddings that accurately capture the multi-node relationships without the decomposing assumptions prevalent in prior methods.

Methodology

The core of Hyper-SAGNN lies in its ability to learn from tuples of node features using self-attention to aggregate information within each tuple of potential hyperedges. This method diverges from the complete decomposition approach found in many existing models, allowing Hyper-SAGNN to maintain the integrity of hyperedges and represent their interactions more naturally and flexibly. Additionally, the model supports arbitrary-sized input, which is crucial for handling non-uniform hypergraphs.

Hyper-SAGNN achieves this by transforming node features into dynamic and static embeddings, which are subsequently used to predict the likelihood that a tuple of nodes forms a hyperedge. Importantly, the approach relies on calculating a form of pseudo-Euclidean distance between these embeddings, affording it a more nuanced representation of the hypergraph's structure.

Evaluation and Performance

The paper provides a comprehensive evaluation of Hyper-SAGNN across multiple datasets, including standard benchmark datasets and single-cell Hi-C datasets in genomics. The results consistently demonstrate that Hyper-SAGNN outperforms the state-of-the-art methods such as DHNE, particularly in hyperedge prediction tasks and outsider identification, a novel task proposed in the paper.

Significant performance gains were observed, especially in tests involving intricate and large-scale hypergraph datasets. The ability of Hyper-SAGNN to handle hypergraphs with varying node and hyperedge sizes makes it especially suitable for domains like genomics, where data is naturally structured in high-order interaction forms.

Implications and Future Directions

The introduction of Hyper-SAGNN provides a robust framework for hypergraph analysis, offering enhanced model scalability and representation capability that could be transformative for applications that inherently involve complex multi-node interactions. Practically, this model could significantly enhance tasks such as knowledge graph completion, recommendation systems, and the analysis of biological data, where the relationships are not merely binary.

Theoretically, the development of Hyper-SAGNN opens pathways for future research into more sophisticated and nuanced models that leverage the self-attention mechanism's strengths, potentially incorporating elements from other areas like reinforcement learning to develop adaptive representations.

Looking forward, potential improvements could include enhancing computational efficiency and extending the model's ability to leverage deeper neighborhood information, presenting opportunities for richer feature extraction and interaction modeling. As hypergraph-based data continues to proliferate in various scientific domains, advancements like Hyper-SAGNN will be critical in harnessing and interpreting these complex datasets effectively.