# Time-Vertex Machine Learning for Optimal Sensor Placement in Temporal Graph Signals: Applications in Structural Health Monitoring

arXiv: https://arxiv.org/abs/2512.19309 · HTML: https://mlsanity.com/paper/2512.19309/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 50 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 14 of 14)

- [How to learn a graph from smooth signals](https://mlsanity.com/paper/1601.02513/) (2016)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [Connecting the Dots: Identifying Network Structure via Graph Signal Processing](https://mlsanity.com/paper/1810.13066/) (2018)
- [Potential, Challenges and Future Directions for Deep Learning in Prognostics and Health Management Applications](https://mlsanity.com/paper/2005.02144/) (2020)
- [Data-Driven Sparse Sensor Placement for Reconstruction](https://mlsanity.com/paper/1701.07569/) (2017)
- [Graph Signal Processing: History, Development, Impact, and Outlook](https://mlsanity.com/paper/2303.12211/) (2023)
- [Random sampling of bandlimited signals on graphs](https://mlsanity.com/paper/1511.05118/) (2015)
- [Eigendecomposition-Free Sampling Set Selection for Graph Signals](https://mlsanity.com/paper/1809.01827/) (2018)
- [Temporal Graph Signal Decomposition](https://mlsanity.com/paper/2106.13517/) (2021)
- [A Computational Framework for Modeling Complex Sensor Network Data Using Graph Signal Processing and Graph Neural Networks in Structural Health Monitoring](https://mlsanity.com/paper/2105.05316/) (2021)
- [Physics-Enhanced Graph Neural Networks For Soft Sensing in Industrial Internet of Things](https://mlsanity.com/paper/2404.08061/) (2024)
- [Global and Local Uncertainty Principles for Signals on Graphs](https://mlsanity.com/paper/1603.03030/) (2016)
- [Optimal Sensor Placement for Source Localization: A Unified ADMM Approach](https://mlsanity.com/paper/2109.03639/) (2021)
- [Informed Graph Learning By Domain Knowledge Injection and Smooth Graph Signal Representation](https://mlsanity.com/paper/2406.03898/) (2024)

## Built on by (most cited first, 2 of 2)

- [Virtual Smart Metering in District Heating Networks via Heterogeneous Spatial-Temporal Graph Neural Networks](https://mlsanity.com/paper/2604.10166/) (2026)
- [WaveGraphNet: Physics-Consistent Guided-Wave Damage Localization through Coupled Inverse-Forward Graph Learning](https://mlsanity.com/paper/2605.20311/) (2026)

## Abstract (arXiv)

Structural Health Monitoring (SHM) plays a crucial role in maintaining the safety and resilience of infrastructure. As sensor networks grow in scale and complexity, identifying the most informative sensors becomes essential to reduce deployment costs without compromising monitoring quality. While Graph Signal Processing (GSP) has shown promise by leveraging spatial correlations among sensor nodes, conventional approaches often overlook the temporal dynamics of structural behavior. To overcome this limitation, we propose Time-Vertex Machine Learning (TVML), a novel framework that integrates GSP, time-domain analysis, and machine learning to enable interpretable and efficient sensor placement by identifying representative nodes that minimize redundancy while preserving critical information. We evaluate the proposed approach on two bridge datasets for damage detection and time-varying graph signal reconstruction tasks. The results demonstrate the effectiveness of our approach in enhancing SHM systems by providing a robust, adaptive, and efficient solution for sensor placement.