# A Time-Vertex Signal Processing Framework

arXiv: https://arxiv.org/abs/1705.02307 · HTML: https://mlsanity.com/paper/1705.02307/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 5 May 2017.

## Built on by (most cited first, 20 of 20)

- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Graph Filters for Signal Processing and Machine Learning on Graphs](https://mlsanity.com/paper/2211.08854/) (2022)
- [Graph Deep Learning for Time Series Forecasting](https://mlsanity.com/paper/2310.15978/) (2023)
- [Synthesizing Decentralized Controllers with Graph Neural Networks and Imitation Learning](https://mlsanity.com/paper/2012.14906/) (2020)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [Graph-Time Convolutional Neural Networks: Architecture and Theoretical Analysis](https://mlsanity.com/paper/2206.15174/) (2022)
- [Graph-Time Convolutional Neural Networks](https://mlsanity.com/paper/2103.01730/) (2021)
- [Learning Product Graphs from Spectral Templates](https://mlsanity.com/paper/2211.02893/) (2022)
- [Graph State-Space Models and Latent Relational Inference](https://mlsanity.com/paper/2301.01741/) (2023)
- [Graph Laplacian Learning with Exponential Family Noise](https://mlsanity.com/paper/2306.08201/) (2023)
- [Beyond Spatio-Temporal Representations: Evolving Fourier Transform for Temporal Graphs](https://mlsanity.com/paper/2402.16078/) (2024)
- [Hyperspectral Image Segmentation based on Graph Processing over Multilayer Networks](https://mlsanity.com/paper/2111.15018/) (2021)
- [Collaborative likelihood-ratio estimation over graphs](https://mlsanity.com/paper/2205.14461/) (2022)
- [Learning Graph ARMA Processes from Time-Vertex Spectra](https://mlsanity.com/paper/2302.06887/) (2023)
- [Edgewise outliers of network indexed signals](https://mlsanity.com/paper/2307.11239/) (2023)
- [Multi-Output Gaussian Processes for Graph-Structured Data](https://mlsanity.com/paper/2505.16755/) (2025)
- [Decorrelating the Future: Joint Frequency Domain Learning for Spatio-temporal Forecasting](https://mlsanity.com/paper/2603.04418/) (2026)
- [Sheaf-theoretic Signal Processing on Graphs: Spectral Theory, Filtering, and Sampling](https://mlsanity.com/paper/2608.01318/) (2026)
- [Role-Specific Predictive Geometries for Nonstationary Multivariate Graph-Signal Forecasting](https://mlsanity.com/paper/2609.06519/) (2026)
- [Signal Processing over Product DAGs: Causal Shifts and Filters](https://mlsanity.com/paper/2609.40275/) (2026)

## Abstract (arXiv)

An emerging way to deal with high-dimensional non-euclidean data is to assume that the underlying structure can be captured by a graph. Recently, ideas have begun to emerge related to the analysis of time-varying graph signals. This work aims to elevate the notion of joint harmonic analysis to a full-fledged framework denoted as Time-Vertex Signal Processing, that links together the time-domain signal processing techniques with the new tools of graph signal processing. This entails three main contributions: (a) We provide a formal motivation for harmonic time-vertex analysis as an analysis tool for the state evolution of simple Partial Differential Equations on graphs. (b) We improve the accuracy of joint filtering operators by up-to two orders of magnitude. (c) Using our joint filters, we construct time-vertex dictionaries analyzing the different scales and the local time-frequency content of a signal. The utility of our tools is illustrated in numerous applications and datasets, such as dynamic mesh denoising and classification, still-video inpainting, and source localization in seismic events. Our results suggest that joint analysis of time-vertex signals can bring benefits to regression and learning.