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

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.

💡 Research Summary

The paper introduces a novel unsupervised ensemble framework for electrocardiogram‑derived respiration (EDR) that combines multiple algorithmic “software sensors” to produce a single, higher‑quality respiratory signal. The authors first preprocess the raw ECG by up‑sampling to 1222 Hz, applying a low‑pass Butterworth filter (cut‑off 32 Hz) and a median filter (422 ms) to suppress noise and baseline wander. High‑accuracy QRS detection yields precise R, S, and Q peak locations, which are used to extract QRS complexes into a matrix that preserves temporal order.

Five families of EDR extraction methods are implemented: (1) traditional RS‑amplitude interpolation, (2) downward slope (DW) of the QRS complex, (3) R‑wave angle (RA), (4) a geometric approach based on the top five principal components (PCA), and (5) a manifold‑learning approach using diffusion maps (DM). Each method is resampled to 10 Hz, resulting in a pool of thirteen candidate EDR signals (one from each of the first three methods, five from PCA, and five from DM).

To avoid contaminating the final ensemble with low‑quality estimates, the authors compute a Respiratory Quality Index (RQI) for each candidate. RQI is defined as the ratio of the maximum power‑spectral peak (MPE) to the total respiratory energy (TRE) within the typical breathing band (0.1–0.75 Hz). Signals with RQI ≥ 0.2 are deemed high‑quality; at least three such signals are required for a valid ensemble. If fewer than three meet the threshold, the highest‑RQI signal from each algorithm family is added to guarantee diversity.

The core technical contribution is the alignment of the selected high‑quality EDR signals using the Graph Connection Laplacian (GCL). Each signal is transformed into a complex analytic signal via the Hilbert transform, producing a phase function p(t). Pairwise inner products ⟨p_i, p_j⟩ yield estimates of relative global phase shifts, which populate a Hermitian matrix T. By constructing the GCL from T and extracting its first non‑trivial eigenvector, the method computes global phase correction terms that bring all signals onto a common phase reference, effectively synchronizing breathing cycles across sensors.

After synchronization, the signals are normalized (detrended and locally rescaled) and simply averaged to generate the final “sync‑ensembled EDR” signal. The authors evaluate the approach on two large whole‑night polysomnography databases comprising over two thousand recordings. Performance is measured with three complementary metrics: (a) γ‑score (synchronised correlation), (b) Optimal Transport (OT) distance (a distributional similarity measure), and (c) Estimated Average Respiratory Rate (EARR) error. The sync‑ensembled EDR consistently outperforms each individual algorithm on all three metrics, with statistical significance (p < 0.001).

A sensitivity analysis isolates the contributions of (i) the RQI‑based sensor selection and (ii) the GCL‑based phase alignment. Removing either component degrades performance markedly, confirming that both quality filtering and synchronization are essential.

The study’s significance lies in three aspects: (1) it provides a fully unsupervised, label‑free method for improving EDR quality, (2) it leverages a mathematically rigorous graph‑theoretic tool (the connection Laplacian) for practical signal alignment, and (3) it demonstrates robustness across noisy ECG recordings and arrhythmic conditions where single‑algorithm EDRs often fail. The authors suggest that the software‑sensor paradigm and the GCL synchronization technique could be extended to other physiological signals such as photoplethysmography, blood pressure, or multimodal wearable data, opening avenues for more reliable, sensor‑agnostic respiratory monitoring in clinical and ambulatory settings.