# Sampling and Reconstruction of Signals on Product Graphs

arXiv: https://arxiv.org/abs/1807.00145 · HTML: https://mlsanity.com/paper/1807.00145/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Jun 2018.

## Built on by (most cited first, 4 of 4)

- [Graph-Time Convolutional Neural Networks](https://mlsanity.com/paper/2103.01730/) (2021)
- [Efficient Signed Graph Sampling via Balancing & Gershgorin Disc Perfect Alignment](https://mlsanity.com/paper/2208.08726/) (2022)
- [Learning Graph ARMA Processes from Time-Vertex Spectra](https://mlsanity.com/paper/2302.06887/) (2023)
- [Windowed Fourier Analysis for Signal Processing on Graph Bundles](https://mlsanity.com/paper/2302.05592/) (2023)

## Abstract (arXiv)

In this paper, we consider the problem of subsampling and reconstruction of signals that reside on the vertices of a product graph, such as sensor network time series, genomic signals, or product ratings in a social network. Specifically, we leverage the product structure of the underlying domain and sample nodes from the graph factors. The proposed scheme is particularly useful for processing signals on large-scale product graphs. The sampling sets are designed using a low-complexity greedy algorithm and can be proven to be near-optimal. To illustrate the developed theory, numerical experiments based on real datasets are provided for sampling 3D dynamic point clouds and for active learning in recommender systems.