Graph-Time Convolutional Autoencoders

Abstract

We introduce graph-time convolutional autoencoder (GTConvAE), a novel spatiotemporal architecture tailored to learn unsupervised representations from multivariate time series on networks. The GTConvAE leverages product graphs to represent the spatiotemporal information and a principled joint convolution operation over this product graph. Instead of fixing the product graph at the outset, we make it parametric to learn also the spatiotemporal coupling for the task at hand, whereas the convolutional filtering parameters learn layer-wise higher-order representations. On top of this, we propose temporal downsampling for the encoder to improve the receptive field in a spatiotemporal manner without affecting the network structure; respectively, in the decoder, we consider the opposite upsampling operator. We prove the GTConvAEs with graph integral Lipschitz filters are stable to relative perturbations in the network structure, ultimately showing the role of the different components in the encoder and decoder on the performance degradation. Numerical experiments for denoising and anomaly detection tasks in power and water networks corroborate our finding and showcase the effectiveness of the GTConv-AE compared with state-of-the-art alternatives.