[Paper Review] A Hypergraph Neural Network Framework for Learning Hyperedge-Dependent Node Embeddings

Ryan Aponte, Ryan A. Rossi+7 more|arXiv (Cornell University)|Dec 28, 2022

Advanced Graph Neural Networks4 citations

TL;DR

This paper proposes Hypergraph Neural Networks (HNN), a novel framework that jointly learns hyperedge embeddings and multiple hyperedge-dependent node embeddings per node, enabling context-aware, higher-order relationship modeling in hypergraphs. HNN achieves state-of-the-art performance, with a mean AUC gain of 7.72% in hyperedge prediction and 11.37% in node classification across diverse datasets.

ABSTRACT

In this work, we introduce a hypergraph representation learning framework called Hypergraph Neural Networks (HNN) that jointly learns hyperedge embeddings along with a set of hyperedge-dependent embeddings for each node in the hypergraph. HNN derives multiple embeddings per node in the hypergraph where each embedding for a node is dependent on a specific hyperedge of that node. Notably, HNN is accurate, data-efficient, flexible with many interchangeable components, and useful for a wide range of hypergraph learning tasks. We evaluate the effectiveness of the HNN framework for hyperedge prediction and hypergraph node classification. We find that HNN achieves an overall mean gain of 7.72% and 11.37% across all baseline models and graphs for hyperedge prediction and hypergraph node classification, respectively.

Motivation & Objective

• To address the limitation of existing hypergraph neural networks that assign a single, uniform embedding to each node, regardless of the hyperedge context.
• To enable more accurate and context-sensitive node representations by learning multiple embeddings per node, each dependent on a specific hyperedge.
• To support data-efficient, flexible, and inductive hypergraph learning for real-world tasks involving noisy or incomplete hyperedges.
• To demonstrate the utility of the framework in novel applications such as design style recommendation using a heterogeneous hypergraph of HTML documents.

Proposed method

• HNN jointly optimizes hyperedge embeddings and a set of hyperedge-dependent node embeddings through an end-to-end, iterative training process.
• Each node is associated with multiple embeddings, where each embedding is specifically conditioned on a distinct hyperedge it participates in.
• The framework does not require a node to be present in a hyperedge to compute its embedding for that hyperedge, enabling inference over absent or unseen relationships.
• It supports inductive learning and can incorporate features on both nodes and hyperedges, enhancing flexibility for diverse downstream tasks.
• A score function (e.g., cosine similarity) is used to compute relevance between fragments and style entities in recommendation tasks.
• The model is trained using a masked training objective and evaluated via metrics like AUC, HR@K, and nDCG on hyperedge prediction and style recommendation tasks.

Experimental results

Research questions

• RQ1 Can a hypergraph neural network learn multiple, context-specific embeddings per node that are dependent on individual hyperedges, improving representation quality?
• RQ2 How does the joint learning of hyperedge and hyperedge-dependent node embeddings affect performance in hyperedge prediction and node classification?
• RQ3 Can the proposed framework generalize to real-world, noisy hypergraphs with incomplete or arbitrary-sized hyperedges?
• RQ4 Does the HNN framework outperform existing baselines in inductive hypergraph learning tasks such as hyperlink prediction and style recommendation?
• RQ5 Can HNN be effectively applied to novel applications like design style recommendation in marketing emails?

Key findings

• HNN achieves a mean AUC gain of 7.72% across all baseline models and graphs in hyperedge prediction tasks.
• In hypergraph node classification, HNN achieves a mean AUC gain of 11.37% over all compared models and datasets.
• For button-style recommendation, HNN achieves an HR@1 of 24.3%, significantly outperforming the next-best model (HyperGCN) at 0.8%.
• In background-style recommendation, HNN achieves an HR@1 of 18.1%, while all baselines fail to exceed 3.1% at HR@10.
• The model demonstrates strong generalization, with HNN achieving the highest nDCG@K scores across all K values in both recommendation tasks.
• The framework is effective even at small K values (e.g., K=1), where baselines like random and popularity perform at 0.00%, highlighting HNN’s precision in top-1 recommendations.