# Unsupervised Ensembling of Multiple Software Sensors with Phase Synchronization: A Robust Approach For Electrocardiogram-derived Respiration

arXiv: https://arxiv.org/abs/2006.13054 · HTML: https://mlsanity.com/paper/2006.13054/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jun 2020.

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

- [Sparsification of the regularized magnetic Laplacian with multi-type spanning forests](https://mlsanity.com/paper/2208.14797/) (2022)
- [Accelerate Vector Diffusion Maps by Landmarks](https://mlsanity.com/paper/2603.21247/) (2026)

## Abstract (arXiv)

Objective: We aimed to fuse the outputs of different electrocardiogram-derived respiration (EDR) algorithms to create one EDR signal that is of higher quality. Methods: We viewed each EDR algorithm as a software sensor that recorded breathing activity from a different vantage point, identified high-quality software sensors based on the respiratory signal quality index, aligned the highest-quality EDRs with a phase synchronization technique based on the graph connection Laplacian, and finally fused those aligned, high-quality EDRs. We refer to the output as the sync-ensembled EDR signal. The proposed algorithm was evaluated on two large-scale databases of whole-night polysomnograms. We evaluated the performance of the proposed algorithm using three respiratory signals recorded from different hardware sensors, and compared it with other existing EDR algorithms. A sensitivity analysis was carried out for a total of five cases: fusion by taking the mean of EDR signals, and the four cases of EDR signal alignment without and with synchronization and without and with signal quality selection. Results: The sync-ensembled EDR algorithm outperforms existing EDR algorithms when evaluated by the synchronized correlation (γ-score), optimal transport (OT) distance, and estimated average respiratory rate (EARR) score, all with statistical significance. The sensitivity analysis shows that the signal quality selection and EDR signal alignment are both critical for the performance, both with statistical significance. Conclusion: The sync-ensembled EDR provides robust respiratory information from electrocardiogram. Significance: Phase synchronization is not only theoretically rigorous but also practical to design a robust EDR.