Efficient and effective graph convolution networks

Abstract

Graph convolution is a generalization of the convolution operation from structured grid data to unstructured graph data. Because any type of data can be represented on a feature graph, graph convolution has been a powerful tool for modeling various types of data. However, such flexibility comes with a price: expensive time and space complexities. Even with state-of-the-art scalable graph convolution algorithms, it remains challenging to scale graph convolution for practical applications. Hence, we propose using Diverse Power Iteration Embeddings (DPIE) to construct scalable graph convolution neural networks. DPIE is an approximated spectral embedding with orders of magnitude faster speed that does not incur additional space complexity, resulting in efficient and effective graph convolution approximation. DPIE-based graph convolution avoids expensive convolution operation in the form of matrix-vector multiplication using the embedding of a lower dimension. At the same time, DPIE generates graphs implicitly, which dramatically reduces space cost when building graphs from unstructured data. The method is tested on various types of data. We also extend the graph convolution to extreme-scale data never-before studied in the graph convolution field. Experiment results show the scalability and effectiveness of DPIE-based graph convolution.