Tensor-view Topological Graph Neural Network

TL;DR

The paper introduces Tensor-view Topological Graph Neural Network (TTG-NN), a novel approach that leverages tensor learning and topological methods to improve graph classification by capturing multi-modal structural information more efficiently.

Contribution

It proposes a new tensor-based topological GNN framework that integrates persistent homology and tensor operations, enhancing structural information capture with reduced computation.

Findings

Outperforms 20 state-of-the-art methods on graph benchmarks

Effectively captures multi-modal topological and structural information

Provides theoretical bounds on approximation errors

Abstract

Graph classification is an important learning task for graph-structured data. Graph neural networks (GNNs) have recently gained growing attention in graph learning and have shown significant improvements in many important graph problems. Despite their state-of-the-art performances, existing GNNs only use local information from a very limited neighborhood around each node, suffering from loss of multi-modal information and overheads of excessive computation. To address these issues, we propose a novel Tensor-view Topological Graph Neural Network (TTG-NN), a class of simple yet effective topological deep learning built upon persistent homology, graph convolution, and tensor operations. This new method incorporates tensor learning to simultaneously capture Tensor-view Topological (TT), as well as Tensor-view Graph (TG) structural information on both local and global levels. Computationally, to fully exploit graph topology and structure, we propose two flexible TT and TG representation learning modules that disentangle feature tensor aggregation and transformation and learn to preserve multi-modal structure with less computation. Theoretically, we derive high probability bounds on both the out-of-sample and in-sample mean squared approximation errors for our proposed Tensor Transformation Layer (TTL). Real data experiments show that the proposed TTG-NN outperforms 20 state-of-the-art methods on various graph benchmarks.