LVCG · Learning Cardiac Latent Representations in Vectorcardiogram Space

The 12-lead ECG is many linear projections of a single 3-D cardiac dipole. LVCG learns view-invariant representations in this physically-grounded latent VCG space.

Abstract

One source, many views

Electrocardiography (ECG) is a cornerstone of cardiac assessment, making the learning of informative ECG representations fundamental to tasks from disease diagnosis to clinical report generation. Yet existing methods operate almost exclusively in the observable ECG signal space. In practice the standard 12-lead ECG is multiple projections of the same underlying cardiac electrical activity from different spatial orientations, so representation learning in the ECG space inevitably introduces substantial redundancy — leading to spurious correlations and a higher risk of overfitting.

Motivated by the Frank vectorcardiogram (VCG) model, we propose learning a unified latent representation of cardiac electrical activity directly in the VCG space. We introduce LVCG, the first general self-supervised framework designed to operate in this physically-grounded latent space. By learning view-invariant latent VCG representations rather than lead-specific artifacts, LVCG minimizes redundancy and improves generalization, consistently outperforming ECG-space baselines — especially under domain shift.

01 The Problem

Observable space, or source space?

A 12-lead ECG is the projection of a cardiac source. The choice is whether to learn from the projection — or from the source behind it.

Observable space

The 12-lead ECG signal

Learn directly on the leads — the signal after projection. Most existing ECG methods live here.

Redundant: leads are linear combinations of one another
Entangled with electrode & device geometry
Encoders overfit the recording setup they were trained on

Source space

The cardiac electrical field

Recover the source first, then learn — before projection. Where LVCG operates.

Compact: no cross-lead redundancy
Decoupled from acquisition geometry
Physically grounded & interpretable

lift ECG → source project source → ECG

Flaw 1 — Deterministic redundancy

Leads are not independent channels

The augmented and third limb leads are exactly recoverable from I and II:

III = II − I · aVR = −(I + II)/2
aVL = I − II/2 · aVF = II − I/2

Feeding all 12 leads as separate channels wastes capacity re-discovering fixed linear relations, and lets predictions violate lead geometry.

Flaw 2 — Geometry entanglement

Signal tangled with acquisition

Waveform morphology depends on how the ECG was recorded, not only on cardiac pathology:

observed waveform = cardiac signal ⊗ acquisition geometry

Electrode placement, body conductivity and device-specific gains all reshape the signal — so encoders generalize poorly across hospitals, devices and populations.

02 The Insight

Learn in the source: the Frank VCG

The single-dipole model treats the whole heart as one time-varying 3-D current vector $v(t)\in\mathbb{R}^3$; each lead is a fixed linear projection of it.

ECG space vs VCG space: leads as projections of one dipole loop

Each lead is a plane cut through one 3-D dipole trajectory $V_t$; P / QRS / T trace their own loops.

Frank VCG — single dipole

$e_\ell(t) = u_\ell^{\top}\, v(t)$

In the observable ECG the P, QRS and T waves overlap on a single line. In the 3-D source space they become cleanly separated loops — VCG keeps the clinically salient structure that projection to leads discards.

Natural separation — every P / QRS / T segment traces its own loop
Learn before projection — no geometry artifacts baked into the features

03 The Method

LVCG — self-supervised learning in VCG space

Lift visible leads into the latent VCG space, encode beat morphology and inter-beat dynamics, then project back to reconstruct the masked leads.

LVCG architecture: beat-level processing, VCG lift/project, encoder and temporal module

Architecture of LVCG

(a) Beat-level processing · (b) VCG-space lift and project · (c) VCG beat encoder + temporal module.

Given visible leads $\mathcal{I}$, LVCG lifts to VCG via Tikhonov least-squares, encodes beat morphology through a token bottleneck, models inter-beat dynamics with a GRU, and projects back to reconstruct the masked leads $\mathcal{J}$. The objective combines ECG reconstruction, VCG reconstruction and temporal consistency:

Training objective

$\mathcal{L}=\mathcal{L}_{\text{ECG}}+\lambda_{\text{vcg}}\mathcal{L}_{\text{VCG}}+\lambda_{\text{temp}}\mathcal{L}_{\text{temp}}$

Partial-lead reconstruction

Observe $K$ leads, recover the full 12-lead ECG through the latent VCG trajectory.

04 The Results

Strongest where labels are scarce

Pretrained on MIMIC-IV-ECG; frozen backbone + linear head across six benchmarks.

1^st

SSL framework in latent VCG space

67.3

best avg AUC@1% across 6 datasets

+10.6

AUC pts on CPSC@1% vs best baseline

0.47

recon MSE, PTB (3→12) vs 1.56 Nef-Net

$Linear-probe performance versus labeled data fraction$

Label efficiency under data scarcity

LVCG is strongest when labels are limited: 67.3 mean Macro-AUROC at 1% labels and 74.5 at 10%, outperforming HeartLang and ST-MEM across the low-label regime. Lines show the six-benchmark mean; bars show per-benchmark results.

Domain shift versus LVCG gain over HeartLang

Gains grow with domain shift

The farther a target dataset is from MIMIC-IV-ECG, the larger LVCG's gain over HeartLang. CPSC2018 is the most shifted target and shows the largest improvement (+10.6 AUC at 1% labels).

Throughput versus linear-probe performance Pareto plot

Accuracy-efficiency Pareto front

LVCG combines high 1%-label AUROC with practical efficiency: 8.3M parameters and about 1.2 ms per sample, much smaller and faster than larger ECG SSL baselines.

Linear Probing — mean test AUC (%)

Method	1%	10%	100%
ST-MEM	56.42	63.39	69.60
HeartLang	63.80	73.39	84.56
LVCG (ours)	67.30	74.54	80.47

+10.6 AUC on CPSC@1% · +4.5 on CSN@1% over the best SSL baseline.

Multi-Lead Reconstruction (3→12)

Method	CPSC MSE↓	PTB MSE↓
Nef-Net	0.68	1.56
LVCG	0.49	0.47

Non-Cardiac Transfer (AUC@1%)

Method	Kidney	Diabetes	Sepsis
HeartLang	58.92	60.41	69.02
LVCG	69.04	63.51	71.68

Ablation — VCG Space Geometry (AUC@1%)

Variant	Super	Sub	Rhythm	CPSC	CSN
ECG Space	51.26	50.34	61.11	50.88	52.53
Learnable Transform	65.02	55.35	52.44	59.14	57.45
Shuffle Direction Matrix	66.54	58.31	62.07	63.12	57.61
LVCG (full)	75.33	70.61	72.03	71.09	62.47

05 Further Analysis

Why it works

Cleaner embeddings, faithful reconstructions, and gains that grow with domain shift.

Embedding structure — t-SNE on CPSC 2018

LVCG separates diagnostic labels more cleanly than ST-MEM and HeartLang under domain shift.

Reconstructed-signal distribution (PCA + KDE)

Reconstructed-signal density (PCA + KDE): LVCG matches ground truth more closely.

Per-lead reconstruction error (MAE) — lower across the board.

Waveform reconstruction examples (PTB, 3→12)

Sample 0000

Sample 0551

Sample 0164

Citation

Cite LVCG

@inproceedings{huang2026lvcg,
  title     = {Learning Cardiac Latent Representations in Vectorcardiogram Space},
  author    = {Huang, Bosong and Zhao, Panzhen and Li, Zengxiang and Lee, Patricia
               and Jin, Wei and Liew, Alan Wee-Chung and Jin, Ming and Pan, Shirui},
  booktitle = {International Conference on Machine Learning (ICML)},
  year      = {2026}
}