Tensor-view Topological Graph Neural Network
Tao Wen, Elynn Chen, Yuzhou Chen
TL;DR
The paper tackles the limitation of conventional GNNs that rely on local neighborhoods by proposing TTG-NN, which fuses persistent-homology-based multi-filtration topology with tensor learning. It introduces two parallel modules, TT-CL for local topological features and TG-CL for global structure, connected through the Tensor Transformation Layer (TTL) that exploits Tucker/CP/TT low-rank decompositions to reduce complexity. The authors provide non-asymptotic, high-probability bounds on both in-sample and out-of-sample mean-squared error under Tucker low-rankness and validate the approach on diverse graph classification benchmarks, achieving state-of-the-art performance and favorable computational efficiency. Overall, TTG-NN substantially improves the integration of topology and tensor-based representations in graphs, with strong empirical gains and solid theoretical guarantees, and offers a flexible framework for further extensions to spatiotemporal and community detection tasks.
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.