Graph-Time Convolutional Autoencoders

We introduce graph-time convolutional autoencoder (GTConvAE), a novel spatiotemporal architecture tailored to unsupervised learning for multivariate time series on networks. The GTConvAE leverages product graphs to represent the time series and a principled joint spatiotemporal convolution over this product graph. Instead of fixing the product graph at the outset, we make it parametric to attend to the spatiotemporal coupling for the task at hand. On top of this, we propose temporal downsampling for the encoder to improve the spatiotemporal receptive field without affecting the network structure; respectively, in the decoder, we consider the opposite upsampling operator. We prove that the GTConvAEs with graph integral Lipschitz filters are stable to relative network perturbations, ultimately showing the role of the different components in the encoder and decoder. Numerical experiments for denoising and anomaly detection in solar and water networks corroborate our findings and showcase the effectiveness of the GTConvAE compared with state-of-the-art alternatives.