# Adaptive Least Mean Squares Estimation of Graph Signals

arXiv: https://arxiv.org/abs/1602.05703 · HTML: https://mlsanity.com/paper/1602.05703/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2016.

## Built on by (most cited first, 13 of 13)

- [Graph Learning: A Survey](https://mlsanity.com/paper/2105.00696/) (2021)
- [Gegenbauer Graph Neural Networks for Time-varying Signal Reconstruction](https://mlsanity.com/paper/2403.19800/) (2024)
- [PySensors: A Python Package for Sparse Sensor Placement](https://mlsanity.com/paper/2102.13476/) (2021)
- [Graph Normalized-LMP Algorithm for Signal Estimation Under Impulsive Noise](https://mlsanity.com/paper/2203.00320/) (2022)
- [LLM-based Online Prediction of Time-varying Graph Signals](https://mlsanity.com/paper/2410.18718/) (2024)
- [LLM Online Spatial-temporal Signal Reconstruction Under Noise](https://mlsanity.com/paper/2411.15764/) (2024)
- [Topological Adaptive Least Mean Squares Algorithms over Simplicial Complexes](https://mlsanity.com/paper/2505.23160/) (2025)
- [Learning Graph ARMA Processes from Time-Vertex Spectra](https://mlsanity.com/paper/2302.06887/) (2023)
- [Adaptive Least Mean Squares Graph Neural Networks and Online Graph Signal Estimation](https://mlsanity.com/paper/2401.15304/) (2024)
- [Graph Signal Adaptive Message Passing](https://mlsanity.com/paper/2410.17629/) (2024)
- [Online Graph Topology Learning via Time-Vertex Adaptive Filters: From Theory to Cardiac Fibrillation](https://mlsanity.com/paper/2411.01567/) (2024)
- [Adaptive Spatio-temporal Estimation on the Graph Edges via Line Graph Transformation](https://mlsanity.com/paper/2311.00656/) (2023)
- [Adaptive Least Mean pth Power Graph Neural Networks](https://mlsanity.com/paper/2405.04111/) (2024)

## Abstract (arXiv)

The aim of this paper is to propose a least mean squares (LMS) strategy for adaptive estimation of signals defined over graphs. Assuming the graph signal to be band-limited, over a known bandwidth, the method enables reconstruction, with guaranteed performance in terms of mean-square error, and tracking from a limited number of observations over a subset of vertices. A detailed mean square analysis provides the performance of the proposed method, and leads to several insights for designing useful sampling strategies for graph signals. Numerical results validate our theoretical findings, and illustrate the performance of the proposed method. Furthermore, to cope with the case where the bandwidth is not known beforehand, we propose a method that performs a sparse online estimation of the signal support in the (graph) frequency domain, which enables online adaptation of the graph sampling strategy. Finally, we apply the proposed method to build the power spatial density cartography of a given operational region in a cognitive network environment.