Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

DPHGNN: A Dual Perspective Hypergraph Neural Networks

Siddhant Saxena, Shounak Ghatak, Raghu Kolla, Debashis Mukherjee, Tanmoy Chakraborty

TL;DR

DPHGNN is proposed, a novel dual-perspective HGNN that introduces equivariant operator learning to capture lower-order semantics by inducing topology-aware spatial and spectral inductive biases.

Abstract

Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral methods based on their design choices. In this work, we analyze the impact of change in hypergraph topology on the suboptimal performance of HGNNs and propose DPHGNN, a novel dual-perspective HGNN that introduces equivariant operator learning to capture lower-order semantics by inducing topology-aware spatial and spectral inductive biases. DPHGNN employs a unified framework to dynamically fuse lower-order explicit feature representations from the underlying graph into the super-imposed hypergraph structure. We benchmark DPHGNN over eight benchmark hypergraph datasets for the semi-supervised hypernode classification task and obtain superior performance compared to seven state-of-the-art baselines. We also provide a theoretical framework and a synthetic hypergraph isomorphism test to express the power of spatial HGNNs and quantify the expressivity of DPHGNN beyond the Generalized Weisfeiler Leman (1-GWL) test. Finally, DPHGNN was deployed by our partner e-commerce company for the Return-to-Origin (RTO) prediction task, which shows ~7% higher macro F1-Score than the best baseline.

DPHGNN: A Dual Perspective Hypergraph Neural Networks

TL;DR

DPHGNN is proposed, a novel dual-perspective HGNN that introduces equivariant operator learning to capture lower-order semantics by inducing topology-aware spatial and spectral inductive biases.

Abstract

Message passing on hypergraphs has been a standard framework for learning higher-order correlations between hypernodes. Recently-proposed hypergraph neural networks (HGNNs) can be categorized into spatial and spectral methods based on their design choices. In this work, we analyze the impact of change in hypergraph topology on the suboptimal performance of HGNNs and propose DPHGNN, a novel dual-perspective HGNN that introduces equivariant operator learning to capture lower-order semantics by inducing topology-aware spatial and spectral inductive biases. DPHGNN employs a unified framework to dynamically fuse lower-order explicit feature representations from the underlying graph into the super-imposed hypergraph structure. We benchmark DPHGNN over eight benchmark hypergraph datasets for the semi-supervised hypernode classification task and obtain superior performance compared to seven state-of-the-art baselines. We also provide a theoretical framework and a synthetic hypergraph isomorphism test to express the power of spatial HGNNs and quantify the expressivity of DPHGNN beyond the Generalized Weisfeiler Leman (1-GWL) test. Finally, DPHGNN was deployed by our partner e-commerce company for the Return-to-Origin (RTO) prediction task, which shows ~7% higher macro F1-Score than the best baseline.
Paper Structure (34 sections, 3 theorems, 12 equations, 8 figures, 10 tables, 1 algorithm)

This paper contains 34 sections, 3 theorems, 12 equations, 8 figures, 10 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Preliminaries, Background and Related Work
  3. Dual Perspective Hypergraph Neural Network (DPHGNN)
  4. Topology-Aware Attention (TAA)
  5. TAA on Spatial Features.
  6. TAA on Spectral Features.
  7. Feature Mixture Module
  8. Dynamic Feature Fusion (DFF)
  9. Time Complexity Analysis
  10. Theoretical Characterization
  11. Equivariant Operator Learning
  12. Expressive Power of DPHGNN
  13. Proof Sketch.
  14. Proof Sketch.
  15. Experiments
  16. ...and 19 more sections

Key Result

proposition 1

The encoding function $f: (X_{\text{HG}}, X_{\text{TAA}}, X_{\text{SIB}})\rightarrow X_{\text{static}}$ learned by equation eq:2 is permutation equivariant, i.e, if $\pi$ is a bijective function; $f(\pi \cdot X)= \pi \cdot f(X)$.

Figures (8)

  • Figure 1: A schematic diagram of our proposed architecture, DPHGNN. Left: Hypergraph decomposition and topology-aware Attention (TAA) mechanism. Middle: Feature Mixture that generates static features by incorporating spectral inductive biases from hypergraph Laplacian smoothing and TAA. Right: Dynamic feature fusion (DFF) that fuses explicitly learned graph embedding in supernodes with the hypergraph message-passing module.
  • Figure 2: Visualization of feature embedding update on the CC-Citeseer dataset (6 classes) -- initial embedding (left), HGNN embedding update (middle), DPHGNN embedding update (right) (see Section \ref{['sec:viz']} for other datasets).
  • Figure 3: Convergence analysis of DPHGNN over benchmark hypergraph and CO-RTO datasets.
  • Figure 4: Generalized version of experimentation pipeline.
  • Figure 5: Deployment details of DPHGNN into our partner e-commerce ecosystem.
  • ...and 3 more figures

Theorems & Definitions (3)

  • proposition 1
  • proposition 2
  • theorem 1