# Kernel-based Reconstruction of Space-time Functions on Dynamic Graphs

arXiv: https://arxiv.org/abs/1612.03615 · HTML: https://mlsanity.com/paper/1612.03615/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2016.

## Built on by (most cited first, 12 of 12)

- [Non-separable Spatio-temporal Graph Kernels via SPDEs](https://mlsanity.com/paper/2111.08524/) (2021)
- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Graph-Time Convolutional Neural Networks](https://mlsanity.com/paper/2103.01730/) (2021)
- [Graph Kalman Filters](https://mlsanity.com/paper/2303.12021/) (2023)
- [Multiple Kernel Representation Learning on Networks](https://mlsanity.com/paper/2106.05057/) (2021)
- [Multilinear Kernel Regression and Imputation via Manifold Learning](https://mlsanity.com/paper/2402.03648/) (2024)
- [Imputation of Time-varying Edge Flows in Graphs by Multilinear Kernel Regression and Manifold Learning](https://mlsanity.com/paper/2409.05135/) (2024)
- [Fluids You Can Trust: Property-Preserving Operator Learning for Incompressible Flows](https://mlsanity.com/paper/2602.15472/) (2026)
- [GKNet: Graph Kalman Filtering and Model Inference via Model-based Deep Learning](https://mlsanity.com/paper/2506.22004/) (2025)
- [Learning Graph ARMA Processes from Time-Vertex Spectra](https://mlsanity.com/paper/2302.06887/) (2023)
- [Forecasting Graph Signals with Recursive MIMO Graph Filters](https://mlsanity.com/paper/2210.15258/) (2022)
- [Reconstruction of Graph Signals on Complex Manifolds with Kernel Methods](https://mlsanity.com/paper/2505.15202/) (2025)

## Abstract (arXiv)

Graph-based methods pervade the inference toolkits of numerous disciplines including sociology, biology, neuroscience, physics, chemistry, and engineering. A challenging problem encountered in this context pertains to determining the attributes of a set of vertices given those of another subset at possibly different time instants. Leveraging spatiotemporal dynamics can drastically reduce the number of observed vertices, and hence the cost of sampling. Alleviating the limited flexibility of existing approaches, the present paper broadens the existing kernel-based graph function reconstruction framework to accommodate time-evolving functions over possibly time-evolving topologies. This approach inherits the versatility and generality of kernel-based methods, for which no knowledge on distributions or second-order statistics is required. Systematic guidelines are provided to construct two families of space-time kernels with complementary strengths. The first facilitates judicious control of regularization on a space-time frequency plane, whereas the second can afford time-varying topologies. Batch and online estimators are also put forth, and a novel kernel Kalman filter is developed to obtain these estimates at affordable computational cost. Numerical tests with real data sets corroborate the merits of the proposed methods relative to competing alternatives.