# Verifying the Smoothness of Graph Signals: A Graph Signal Processing Approach

arXiv: https://arxiv.org/abs/2305.19618 · HTML: https://mlsanity.com/paper/2305.19618/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 May 2023.

## Built on by (most cited first, 6 of 6)

- [GSP-KalmanNet: Tracking Graph Signals via Neural-Aided Kalman Filtering](https://mlsanity.com/paper/2311.16602/) (2023)
- [Leveraging Low-rank Factorizations of Conditional Correlation Matrices in Graph Learning](https://mlsanity.com/paper/2506.10628/) (2025)
- [Cramer-Rao Bounds for Laplacian Matrix Estimation](https://mlsanity.com/paper/2504.04576/) (2025)
- [Estimating Fair Graphs from Graph-Stationary Data](https://mlsanity.com/paper/2510.07536/) (2025)
- [Rotation-Parameterized Graph Fractional Fourier Transform: Definition, Properties, and Optimal Filtering](https://mlsanity.com/paper/2511.16111/) (2025)
- [Delving into Non-Exchangeability for Conformal Prediction in Graph-Structured Multivariate Time Series](https://mlsanity.com/paper/2605.04957/) (2026)

## Abstract (arXiv)

Graph signal processing (GSP) deals with the representation, analysis, and processing of structured data, i.e. graph signals that are defined on the vertex set of a generic graph. A crucial prerequisite for applying various GSP and graph neural network (GNN) approaches is that the examined signals are smooth graph signals with respect to the underlying graph, or, equivalently, have low graph total variation (TV). In this paper, we develop GSP-based approaches to verify the validity of the smoothness assumption of given signals (data) and an associated graph. The proposed approaches are based on the representation of network data as the output of a graph filter with a given graph topology. In particular, we develop two smoothness detectors for the graph-filter-output model: 1) the likelihood ratio test (LRT) for known model parameters; and 2) a semi-parametric detector that estimates the graph filter and then validates its smoothness. The properties of the proposed GSP-based detectors are investigated, and some special cases are discussed. The performance of the GSP-based detectors is evaluated using synthetic data, data from the IEEE 14-bus power system, and measurements from a network of light intensity sensors, under different setups. The results demonstrate the effectiveness of the proposed approach and its robustness to different generating models, noise levels, and number of samples.