[Paper Review] Tensor graph convolutional neural network

Tong Zhang, Wenming Zheng+2 more|arXiv (Cornell University)|Mar 27, 2018

Advanced Graph Neural Networks19 references10 citations

TL;DR

This paper proposes a Tensor Graph Convolutional Neural Network (TGCNN) that efficiently performs graph convolution on factorizable graphs—specifically sequential dynamic graphs (e.g., skeleton action recognition) and cross-attribute graphs (e.g., matrix completion for recommendation systems). By introducing a parameterized Kronecker sum operation and a graph preserving layer with cross graph convolution and graph pooling, TGCNN reduces computational and memory costs while enabling recursive, global modeling of spatio-temporal and cross-attribute relationships, achieving state-of-the-art performance on NTU RGB+D, LSC, and Synthetic 'Netflix' datasets.

ABSTRACT

In this paper, we propose a novel tensor graph convolutional neural network (TGCNN) to conduct convolution on factorizable graphs, for which here two types of problems are focused, one is sequential dynamic graphs and the other is cross-attribute graphs. Especially, we propose a graph preserving layer to memorize salient nodes of those factorized subgraphs, i.e. cross graph convolution and graph pooling. For cross graph convolution, a parameterized Kronecker sum operation is proposed to generate a conjunctive adjacency matrix characterizing the relationship between every pair of nodes across two subgraphs. Taking this operation, then general graph convolution may be efficiently performed followed by the composition of small matrices, which thus reduces high memory and computational burden. Encapsuling sequence graphs into a recursive learning, the dynamics of graphs can be efficiently encoded as well as the spatial layout of graphs. To validate the proposed TGCNN, experiments are conducted on skeleton action datasets as well as matrix completion dataset. The experiment results demonstrate that our method can achieve more competitive performance with the state-of-the-art methods.

Motivation & Objective

• To address the high computational and memory cost of standard graph convolution on large, factorizable graphs such as dynamic skeletons and cross-attribute networks.
• To develop a recursive learning mechanism that globally models spatio-temporal and cross-graph relationships across subgraphs.
• To improve performance on graph-structured data by jointly modeling spatial, temporal, and cross-attribute dependencies.
• To reduce computational burden through tensor-based operations that decompose large adjacency matrices into smaller, manageable components.

Proposed method

• Introduces a graph preserving layer that recursively maintains salient nodes from previously processed subgraphs and integrates them with incoming graphs.
• Employs a parameterized Kronecker sum operation to learn an optimal conjunctive adjacency matrix that models relationships between nodes across two subgraphs.
• Uses cross graph convolution based on the Kronecker sum to efficiently perform graph filtering on smaller matrices, reducing memory and computation costs.
• Applies graph pooling within the graph preserving layer to select and retain only the most salient nodes for the next recursive step.
• Utilizes a recursive tensor convolution framework to encode both spatial layout and temporal dynamics in sequential graphs.
• Employs polynomial approximation for graph filtering in the spectral domain, with adjustable order K for tuning model capacity.

Experimental results

Research questions

• RQ1 Can a recursive graph convolution framework effectively model spatio-temporal dependencies in dynamic skeleton sequences while maintaining computational efficiency?
• RQ2 How does the parameterized Kronecker sum operation improve performance over standard Kronecker sum or isolated graph convolution in cross-attribute graph learning?
• RQ3 To what extent does the graph preserving layer with cross graph convolution and graph pooling enhance global graph representation learning across factorized subgraphs?
• RQ4 How does the choice of polynomial order K in spectral filtering affect performance on graph-structured data?

Key findings

• TGCNN achieves 86.6% precision and 82.9% recall on the LSC dataset under the RCSub protocol, outperforming IGCNN (80.4% precision, 77.7% recall).
• On the Synthetic 'Netflix' dataset, TGCNN achieves an RMS error of 0.0042, surpassing RGCNN (0.0053) and sRGCNN (0.0106), demonstrating superior matrix completion performance.
• The parameterized Kronecker sum operation improves performance over the classic Kronecker sum, achieving 86.6% precision and 82.9% recall compared to 85.2% and 82.4% respectively.
• The optimal polynomial order K for graph filtering is 2 for precision and 5 for recall on the LSC dataset, indicating sensitivity to hyperparameter choice.
• TGCNN significantly outperforms isolate graph CNN (IGCNN), confirming the effectiveness of recursive, cross-graph learning over isolated subgraph processing.
• The graph preserving layer enables global modeling of factorized graphs by retaining and reusing salient nodes across recursive steps, enhancing representation learning.