Research question
Can a compact kernel combine angular similarity and distance from a normal reference to classify ECG beats with an inspectable decision geometry?
Condensed abstract
The study introduces a classically simulated quantum angle–distance kernel (QADK). Engineered morphology, spectral, and phase features are encoded as complex vectors; fidelity and reference-relative distance form a kernel used with support vector machines for supervised classification and one-class anomaly detection.
Key contribution
A decomposable kernel joining angular alignment with deviation from a normal reference, evaluated with repeated patient-level splits, anomaly detection, ablations, and computational analysis.
My contribution
The published author-contribution statement credits Arman Salehi with writing and generating the computational code.
Method overview
Each heartbeat is summarized by eight morphology, spectral, and phase descriptors. A parameterized encoding maps the vector into a complex state. The kernel combines squared fidelity with a reference-relative projection gap, producing a Gram matrix for an SVM.
Interactive method figure
Two measurements, one kernel
- Angular alignment
- Reference-relative distance
- Heartbeat x
- Heartbeat y
- Normal reference
Dataset and evaluation
Data
The paper evaluates pre-segmented, 187-sample ECG heartbeats from the ECG Heartbeat Categorization dataset, using the PTB diagnostic records for the binary normal-versus-pathological task.
Protocol
The supervised study reports 100 patient-level Monte Carlo 80/20 splits, alongside one-class anomaly detection, ablation studies, sensitivity analysis, and comparisons with linear and RBF SVMs, a 1D CNN, and an MLP.
Main results
QADK-SVM reported AUC-ROC 0.977 ± 0.003, macro F1 0.923 ± 0.005, and accuracy 0.937 ± 0.004. One-class anomaly detection reported AUC 0.884 ± 0.005.
Baseline comparison
The reported QADK model clearly exceeded the linear SVM and MLP on headline measures. The RBF SVM retained a small lead before embedding adjustment; the paper reports that tuning the embedding reduced that gap below 0.5 percentage points.
Limitations and failure modes
- All quantum operations were simulated classically; no quantum hardware was evaluated.
- Gram-matrix construction scales quadratically with sample count.
- The model uses engineered heartbeat descriptors rather than end-to-end raw-signal learning.
- Unsupervised clustering remained weak, and prospective clinical utility or external-site generalization was not established.
Reproducibility resources
The paper-associated computational material is available as a versioned Zenodo artifact. The source data are described at ECG Heartbeat Categorization dataset (PTB records).
Verification sources
Cite this work
Arman Salehi, Hamid Reza Goudarzi, Ashkan Heydarian (2026). Quantum Angle–distance kernel for ECG classification and anomaly detection: a quantum-inspired framework for biomedical signal analysis. BioData Mining, 19, Article 14. https://doi.org/10.1186/s13040-026-00519-3
BibTeX
@article{salehi2026qadk,
title = {Quantum Angle–distance kernel for ECG classification and anomaly detection: a quantum-inspired framework for biomedical signal analysis},
author = {Arman Salehi and Hamid Reza Goudarzi and Ashkan Heydarian},
year = {2026},
doi = {10.1186/s13040-026-00519-3},
journal = {BioData Mining},
volume = {19},
article-number = {14},
publisher = {Springer Nature}
}Publication record last verified 2026-07-26.