# Spatiotemporal Covariance Neural Networks

arXiv: https://arxiv.org/abs/2409.10068 · HTML: https://mlsanity.com/paper/2409.10068/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 16 Sep 2024.

## Builds on (most cited first, 20 of 20)

- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Graph Neural Network for Traffic Forecasting: A Survey](https://mlsanity.com/paper/2101.11174/) (2021)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Stability Properties of Graph Neural Networks](https://mlsanity.com/paper/1905.04497/) (2019)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [Multivariate Time Series Forecasting with Dynamic Graph Neural ODEs](https://mlsanity.com/paper/2202.08408/) (2022)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Learning Fast and Slow for Online Time Series Forecasting](https://mlsanity.com/paper/2202.11672/) (2022)
- [Stationary Graph Processes and Spectral Estimation](https://mlsanity.com/paper/1603.04667/) (2016)
- [Stationary signal processing on graphs](https://mlsanity.com/paper/1601.02522/) (2016)
- [Forecasting Time Series with VARMA Recursions on Graphs](https://mlsanity.com/paper/1810.08581/) (2018)
- [coVariance Neural Networks](https://mlsanity.com/paper/2205.15856/) (2022)
- [Explainable Brain Age Prediction using coVariance Neural Networks](https://mlsanity.com/paper/2305.18370/) (2023)
- [Algorithms for Learning Graphs in Financial Markets](https://mlsanity.com/paper/2012.15410/) (2020)
- [Fast Robust PCA on Graphs](https://mlsanity.com/paper/1507.08173/) (2015)
- [Online Principal Component Analysis in High Dimension: Which Algorithm to Choose?](https://mlsanity.com/paper/1511.03688/) (2015)
- [Deep Statistical Solver for Distribution System State Estimation](https://mlsanity.com/paper/2301.01835/) (2023)
- [Transferability of coVariance Neural Networks and Application to Interpretable Brain Age Prediction using Anatomical Features](https://mlsanity.com/paper/2305.01807/) (2023)

## Built on by (most cited first, 9 of 9)

- [Sparse Covariance Neural Networks](https://mlsanity.com/paper/2410.01669/) (2024)
- [Covariance Density Neural Networks](https://mlsanity.com/paper/2505.11139/) (2025)
- [Disentangling Neurodegeneration with Brain Age Gap Prediction Models: A Graph Signal Processing Perspective](https://mlsanity.com/paper/2510.12763/) (2025)
- [Learning with Covariance Matrices: Principal Component Analysis Meets Learning with Graphs](https://mlsanity.com/paper/2609.10490/) (2026)
- [Explainable Brain Age Gap Prediction in Neurodegenerative Conditions using coVariance Neural Networks](https://mlsanity.com/paper/2501.01510/) (2025)
- [Precision Neural Networks: Joint Graph And Relational Learning](https://mlsanity.com/paper/2509.14821/) (2025)
- [CoVariance Filters and Neural Networks over Hilbert Spaces](https://mlsanity.com/paper/2509.13178/) (2025)
- [Spatiotemporal Kronecker Covariance Neural Networks](https://mlsanity.com/paper/2609.25326/) (2026)
- [Joint Precision Neural Networks: Task-Aware Dependency and Predictive Learning](https://mlsanity.com/paper/2610.06023/) (2026)

## Abstract (arXiv)

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.