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.

翻译：图分类是图结构数据的重要学习任务。近年来，图神经网络在图学习中日益受到关注，并在许多重要图问题上展现出显著改进。尽管现有图神经网络已达到最优性能，但它们仅利用每个节点周围极有限邻域的局部信息，导致多模态信息缺失和计算开销过大。为解决这些问题，我们提出了一种新型张量视角拓扑图神经网络（TTG-NN），这是一类基于持续同调、图卷积和张量运算的简单而有效的拓扑深度学习模型。该新方法融合张量学习，能够同时捕捉局部和全局层面上的张量视角拓扑结构信息与张量视角图结构信息。在计算方面，为充分利用图拓扑与结构，我们提出了两种灵活的TT与TG表示学习模块，该模块解耦特征张量聚合与变换，并以更少计算量学习保留多模态结构。在理论方面，我们推导了所提出的张量变换层在样本外和样本内均方逼近误差的高概率上界。真实数据实验表明，所提出的TTG-NN在各种图基准测试中优于20种最先进方法。