Graph Classification Gaussian Processes via Spectral Features

Felix Opolka, Yin-Cong Zhi, Pietro Lio, Xiaowen Dong

Keywords: Gaussian processes, graph classification, spectral features, graph signal processing

TL;DR: Combining Gaussian processes with spectral features of attributed graphs leads to surprisingly strong performance for the task of graph classification.

Abstract: Graph classification aims to categorise graphs based on their structure and node attributes. In this work, we propose to tackle this task using tools from graph signal processing by deriving spectral features within the framework of Bayesian modelling with Gaussian processes. We present two variants of spectral Gaussian processes for graph classification. The first variant uses spectral features based on the distribution of energy of a node feature signal over the spectrum of the graph. We show that even such a simple approach, having no learnt parameters, can yield competitive performance compared to strong neural network and graph kernel baselines. A second, more sophisticated variant is designed to capture multi-scale and localised patterns in the graph by learning spectral graph wavelet filters, obtaining improved performance on synthetic and real-world data sets. Finally, we show that both models produce well calibrated uncertainty estimates, enabling reliable decision making based on the model predictions.