Spatiotemporal Kronecker Covariance Neural Networks

2026-09-21

AI Summary

为解决多变量时间序列中时空模式识别问题，提出Kronecker协方差神经网络(KVNN)，通过分解时空依赖性，实现非线性处理与稳定性。

Abstract

Multivariate time series contain complex patterns that span across both space and time. While covariance-based statistical tools like spatiotemporal Principal Component Analysis (ST-PCA) help identify these patterns, they are limited to linear operations and prone to estimation errors with limited data. Recent covariance-based spatiotemporal neural networks offer more stable, non-linear alternatives, but they ignore correlations across different time steps. To solve this, we introduce the Kronecker coVariance Neural Network (KVNN), a temporal graph neural network that represents the spatiotemporal covariance matrix via a sum of Kronecker products where spatial and temporal dependencies are decoupled. By implementing filtering operations on spatial and temporal components, KVNNs achieve expressive processing capabilities, admit a rigorous spectral analysis, and are provably stable to finite-sample estimation errors, ultimately addressing all of ST-PCA's limitations. We show on five real-world datasets that KVNNs achieve strong forecasting performance, often requiring significantly fewer trainable parameters than competitive methods, and are consistent under estimation noise.

Problem

• spatiotemporal covariance
• estimation errors
• non-linear alternatives
• temporal correlations

Innovation

• Kronecker Covariance Neural Network
• spatiotemporal covariance matrix
• temporal graph neural network
• Kronecker product