Spatiotemporal Covariance Neural Networks

TL;DR

This paper introduces STVNN, a neural network model that effectively captures spatiotemporal dependencies in multivariate time series by operating on covariance matrices, offering stability and adaptability in streaming data scenarios.

Contribution

The paper proposes STVNN, a novel relational learning model that leverages covariance matrices and graph convolutions, with proven stability and improved performance over PCA-based methods.

Findings

STVNN is stable to online covariance estimation uncertainties.

STVNN outperforms temporal PCA in dynamic, streaming data settings.

Experimental results show STVNN adapts well to changing data distributions.

Abstract

Modeling spatiotemporal interactions in multivariate time series is key to their effective processing, but challenging because of their irregular and often unknown structure. Statistical properties of the data provide useful biases to model interdependencies and are leveraged by correlation and covariance-based networks as well as by processing pipelines relying on principal component analysis (PCA). However, PCA and its temporal extensions suffer instabilities in the covariance eigenvectors when the corresponding eigenvalues are close to each other, making their application to dynamic and streaming data settings challenging. To address these issues, we exploit the analogy between PCA and graph convolutional filters to introduce the SpatioTemporal coVariance Neural Network (STVNN), a relational learning model that operates on the sample covariance matrix of the time series and leverages joint spatiotemporal convolutions to model the data. To account for the streaming and non-stationary setting, we consider an online update of the parameters and sample covariance matrix. We prove the STVNN is stable to the uncertainties introduced by these online estimations, thus improving over temporal PCA-based methods. Experimental results corroborate our theoretical findings and show that STVNN is competitive for multivariate time series processing, it adapts to changes in the data distribution, and it is orders of magnitude more stable than online temporal PCA.