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.
From heartbeats to geometry
Baseline and current
The baseline stays fixed. Both figures use the same scales.
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
A small, inspectable implementation of the two-dimensional kernel arithmetic.
Worked example checkedChecked locally 2026-09-05 · bundle v1.0.0
- Paper-associated code
- Zenodo record 17652604 This external archive is separate from the small check below. Its full environment was not executed here.
- Inputs for this check
- Two teaching angles, 60° and 90°, with equal weights. No ECG records are needed.
- Prerequisites
- Python 3.10+ · standard library only · CPU · no network or large dataset download. A notebook environment is optional.
- Full study data
- ECG Heartbeat Categorization dataset (PTB records) Consult the paper and dataset documentation before attempting the full study.
Run the small check
- Download and extract the complete bundle.
- Open a terminal in the extracted folder and run
python check.py. - Evaluate fidelity, the squared reference-projection gap, and their weighted sum. Compare every value with the supplied expected output.
Includes Python, an equivalent notebook, source JSON, expected output, and SHA-256 provenance. The notebook runs from the extracted folder.
Expected output and individual files
F = 0.933013 · D = 0.025255 · K = 0.479134
What this does not establish
This does not reproduce feature extraction, patient-wise splits, model training, or ECG accuracy. The equal normalized weights belong to this teaching example.
These checks use the portfolio’s existing sourced records. External archive links could not be freshly rechecked during package preparation. A passing check is not a full-paper replication.
The decisions behind the method
A research note on similarity geometry, patient-wise evaluation, and what the QADK study does—and does not—show.
Read the research noteVerification 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.
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