I-GraphECG: Observability-Based Lead Selection and Interpretable Disease Prediction from the 12-Lead ECG Using a Gray-Box Graph Electrophysiology Surrogate

Figures

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  Figure 1. Overview of I-GraphECG. An observed 12-lead median-beat ECG y(t) is mapped by the encoder Eψ (an amortized approximation to a constrained parameter estimator) to a bounded set of equivalent electrophysiological descriptors θ^∈R47 (Equation (1)). The descriptors drive a graph electrophysiology decoder Dθ^ (Equations (3)–(7)) in which activation times propagate along an explicit directed conduction graph (δj=δroot+∑e∈path(j)de), generate per-node double-sigmoid waveforms, and are projected to the body surface through a constrained low-rank lead-field (H=AB, rank three) to reconstruct the 12-lead signal y^(t) under the reconstruction constraint y^≈y. Disease prediction uses a classifier C (Equation (1)) acting on interpretable descriptors ϕ(θ^,y^)—conduction (QRS-duration), repolarization (APD), T-wave morphology, and lead-projected ST—rather than on the raw waveform.

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  Figure 2. Representative reconstructions. Observed (black) versus reconstructed (red) median beats in leads I, II, V2 and V5 for one test record per class (NORM, MI, STTC, CD). The model captures beat morphology (overall median correlation 0.91; a full 12-lead example in Figure S2); absolute-amplitude detail (deep S waves, some T-wave peaks) remains approximate, consistent with the scaled NRMSE ≈0.40; frontal-lead reconstruction is weaker than precordial (lead I, left column), and the P-wave is not reconstructed (Section 3.2). The dotted vertical line in each panel marks the R peak (t=0).

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  Figure 3. Classification performance of the interpretable feature groups (fold-10 test, seed-42; points are macro-AUROC, error bars 95% bootstrap CIs). The five θ-based variants (C0, C2–C5) cluster near 0.90; the reduced 31-descriptor set C6 sits below them. Dashed/dotted lines mark the black-box reference (hand-crafted + XGBoost 0.9200, ResNet1D 0.9241). The y-axis is truncated to 0.87–0.93 for visualization only; error bars are marginal CIs, not a pairwise test (Section 3.4).

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  Figure 4. Per-class confusion matrix of the main interpretable model at the argmax operating point (C5, seed-42, fold-10 test); rows are true classes, normalized to sum to one.

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  Figure 5. Core interpretable descriptors by diagnostic class (PTB-XL fold-10 test). (a) QRS-duration measured on the reconstructed waveform; higher in CD (Cliff’s δ=+0.53±0.02 across five seeds). (b) Cross-lead T-wave sign discordance, computed on the observed ECG; higher in STTC (δ=+0.753, identical across seeds). (c) T-peak maximum absolute amplitude, observed ECG; lower in STTC (δ=−0.531). (d) Lead-projected ST maximum absolute value, a parameter-derived quantity in the decoder’s scaled lead units; weak and seed-variable in MI (signed δ=−0.19±0.18), retained as the observability-limited negative example. Boxes show the interquartile range and median, whiskers extend to 1.5 × IQR, and points beyond the whiskers are not drawn. Cliff’s δ is versus NORM; the accompanying Kruskal–Wallis p-values are FDR-corrected (Section 2.11).

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  Figure 6. Lead-set identifiability: how much each lead set can recover (test subset, 400 records; error bars are the standard deviation across five training seeds). (a) Spectral-entropy effective rank of the Fisher information matrix against the number of leads; it measures spectral spread and is not itself monotone in lead count. The two faint lines are nested reduction chains (12 leads ⊃ a three-lead set ⊃ lead II); the three-lead sets, none of which contains another, are plotted side by side. The star marks the identity-noise optimum I+V1+V4, optimal under that noise model only (Section 3.7). The vertical spread at three leads shows how much lead choice matters at a fixed lead count; the 12-lead point uses all 12 displayed leads under Σ=I (Section 2.8). (b) Mean identifiability score by parameter group (log scale); the internal ST-source αST is least identifiable by one and a half to two orders of magnitude.

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  Figure 7. Observability-based lead selection: which leads to keep (test subset, 400 records, seed-42; identity-noise model throughout—under the empirical-noise covariance the optimum is a different triple, Section 3.7). (a) Three-lead selection under identity noise: logdetFλ of the three best sets from an exhaustive search over all 56 subsets of the eight independent leads, with the clinical set II+V1+V5 shown for scale. Error bars are omitted because the bootstrap resamples records jointly for every set; the defined uncertainty is that of the paired difference against the clinical set (+9.98 point estimate; bootstrap mean +10.00, 95% CI [9.81,10.21]; +32.38 under the empirical weighting). The 0.45 margin over the second-ranked set is of the order of its between-seed variation, which is why the third lead does not reproduce across training seeds. (b) Marginal log det contribution of each lead in the selected set; large and comparable contributions indicate low redundancy and spatial complementarity.