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arxiv: 2607.05282 · v1 · pith:3T6TQ56S · submitted 2026-07-06 · eess.SP · cs.AI· cs.LG· stat.ME

Wavelet Scattering Transform for Interpretable Schizophrenia Biomarker Discovery and Classification from Resting-State EEG

Md. Taksimul Ahsan Tawhid , Nasif Ahmed Rafe , Alif Tahmid Priyom , K. M. Mustafizur Rahman This is my paper

Reviewed by Pith2026-07-07 19:46 UTCglm-5.2pith:3T6TQ56Sopen to challenge →

classification eess.SP cs.AIcs.LGstat.ME
keywords Wavelet Scattering TransformschizophreniaEEG biomarkercross-frequency couplingamplitude modulationLOSO cross-validationSHAP explainabilityresting-state EEG
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The pith

Schizophrenia's EEG signature lives in cross-frequency amplitude modulation, not raw power

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper argues that the electrophysiological signature of schizophrenia is not primarily a change in how much power each brain rhythm has, but rather a disruption in how brain rhythms modulate each other over time — a property captured by second-order coefficients of the Wavelet Scattering Transform (WST). The WST decomposes an EEG signal into a hierarchy: zeroth-order coefficients capture slow baseline drift, first-order coefficients capture band-specific energy (like a robust spectrogram), and second-order coefficients capture how the amplitude envelope of a fast rhythm is itself modulated by slower rhythms — i.e., cross-frequency coupling. Applying this to resting-state EEG from 84 adolescent subjects (45 schizophrenia, 39 healthy controls), the authors find that 78.5% of the statistically significant biomarkers surviving false-discovery-rate correction are second-order coefficients, concentrated in the gamma band, with electrode P3 (left parietal) as the single most discriminative recording site. Under strict leave-one-subject-out cross-validation — which prevents the temporal data leakage the authors argue inflates prior work — a Random Forest classifier on the full WST feature space achieves 90.48% accuracy (AUC 0.934, sensitivity 95.56%). SHAP explainability analysis independently confirms that the model's decisions center on the same parietal-occipital and right-frontal regions identified by the statistical biomarker analysis. The paper's central claim is that schizophrenia is measurable as a disorder of multi-scale temporal coordination — disrupted amplitude modulation dynamics — rather than a disorder of altered mean spectral power, and that the WST provides a principled, interpretable feature space for capturing this.

Core claim

The dominant discriminative biomarkers for schizophrenia in resting-state EEG are second-order wavelet scattering coefficients — features that quantify cross-frequency amplitude modulation — rather than first-order spectral energy features. Of 1,255 features surviving Benjamini–Hochberg false-discovery-rate correction, 78.5% are second-order, 57.9% fall in the gamma band, and the left parietal electrode P3 produces the most top-ranked biomarkers. Schizophrenia patients show a systematic, near-universal reduction (99.8% of significant features with negative effect sizes) in scattering energy, with the largest deficit at P3 (Cohen's d = −1.19, a 28.7% drop). This pattern — cross-frequency-coug

What carries the argument

Wavelet Scattering Transform (WST): a hierarchical signal decomposition that cascades wavelet convolutions with modulus and averaging operations. Zeroth-order coefficients (S0) capture local DC baseline; first-order (S1) capture band-limited spectral energy; second-order (S2) capture amplitude modulation of one frequency band by another (cross-frequency coupling). Configured here with invariance scale J=7 (1-second window) and quality factors Q=(8,1), yielding 176 scattering paths per epoch across 16 EEG channels.

Load-bearing premise

The entire framework is validated on a single dataset of 84 adolescent subjects with no medication controls, no multi-site replication, and no adult cohort. The claim that disrupted amplitude modulation is the primary electrophysiological signature of schizophrenia rests on this one sample. Additionally, the SHAP and ANOVA biomarker rankings show only moderate concordance (Spearman ρ = 0.429, p = 0.097), meaning the two methods agree on the general spatial pattern but not on

What would settle it

If second-order WST coefficients no longer dominate the discriminative biomarker set when tested on an independent, multi-site adult dataset with medication-naive patients — or if the P3/gamma-band concentration fails to replicate — the central claim that amplitude modulation disruption is the primary electrophysiological signature of schizophrenia would not hold beyond this cohort.

Figures

Figures reproduced from arXiv: 2607.05282 by Alif Tahmid Priyom, K. M. Mustafizur Rahman, Md. Taksimul Ahsan Tawhid, Nasif Ahmed Rafe.

Figure 1
Figure 1. Figure 1: Overview of the proposed methodological workflow for EEG-based schizophrenia 2 𝐽 samples. In neural signals, 𝑆0 is the local DC baseline or Slow Cortical Potential (SCP). It represents the ultra-slow, averaged electrical drift of large populations of neurons over the time window defined by 2 𝐽 . First-order (𝑆1 ): 𝑆1𝑥(𝑡, 𝜆1 ) = |𝑥 ⋆ 𝜓𝜆1 | ⋆ 𝜙𝐽 (𝑡) (4) 𝜓𝜆1 (𝑡)complex-valued analytic Morlet wavelet at wavele… view at source ↗
Figure 2
Figure 2. Figure 2: Hierarchical representation of multi-order WST coefficient extraction across different wavelet frequencies. 𝐹 (𝑑) = 𝑆𝑆(𝑑) 𝐵 ∕1 𝑆𝑆(𝑑) 𝑊 ∕82 (7) 2.4.2. Multiple Testing Correction Multiple testing correction is essential to control the false discovery rate. The Benjamini-Hochberg (BH) procedure[47] was selected as the primary correction method. The 𝑝-values corresponding to 𝐹 (𝑑) be sorted in ascending order… view at source ↗
Figure 3
Figure 3. Figure 3: EEG signal preprocessing and epoch segmentation stages for channel F7: (a) raw versus zero-phase Butterworth bandpass filtered profiles, and (b) isolated 256-sample stationary epoch tracking localized voltage fluctuations. naturally handles high-dimensional feature spaces, provides inherent feature importance estimates that can be cross￾referenced with the statistical biomarker analysis, and is robust to c… view at source ↗
Figure 4
Figure 4. Figure 4: Statistical biomarker identification and multiple testing correction profiles for subject-level feature analysis: (a) distribution of raw feature 𝑝-values against uncorrected and Bonferroni thresholds, (b) total discovery yield comparison demonstrating strictness across standard multiple testing adjustments, (c) volcano topology mapping feature discriminative scores against − log10(𝑝−𝑣𝑎𝑙𝑢𝑒) highlights wher… view at source ↗
Figure 5
Figure 5. Figure 5: Spatial-spectral characterization and discriminative mapping of statistically significant biomarkers: (a) density distribution of discovered features mapping individual recording channels across classical EEG frequency bands, (b) localized statistical variance tracking mean 𝐹-scores over consolidated brain subdivisions, and (c) power spectral directional variance profiling group-level percentage activity f… view at source ↗
Figure 6
Figure 6. Figure 6: Two-dimensional topographic mapping of spatial brain activity alterations: (a) raw baseline comparison displaying mean WST feature values across the electrode grid for Healthy Controls (left) and Schizophrenia Patients (right), and (b) diagnostic variance mapping profiling localized variations through absolute signal divergence (left) and group-level directional percentage scaling (right) across distinct c… view at source ↗
Figure 7
Figure 7. Figure 7: ROC curves for subject-independent schizophrenia classification under LOSO cross-validation (a) Random Forest subject-level predictions. (b) Support Vector Machine (SVM) subject-level predictions [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Confusion matrices evaluated over subject-level Leave-One-Subject-Out Cross-Validation (LOSO-CV, 𝑛 = 84). strong spatial concordance with the biomarker density map; electrode 𝑃 3, positioned directly over the left parietal core of the fronto-parietal network, emerged as the single most affected node, yielding the majority of the top-ranked fea￾tures [PITH_FULL_IMAGE:figures/full_fig_p009_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Per-subject classification profiles and prediction probability maps under LOSO-CV, comparison between (a) the Random Forest classifier and (b) the Support Vector Machine (SVM) with an RBF kernel [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: SHAP summary beeswarm plot of the top 20 most discriminative Wavelet Scattering Transform features (a) Normalized mean |SHAP| values aggregated per channel. (b) Spatial distribution of SHAP importance across the scalp [PITH_FULL_IMAGE:figures/full_fig_p011_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: Spatial aggregation and channel-level SHAP importance mapping (a) Horizontal bar chart detailing feature importance summed across all scattering paths per electrode, where colors signify distinct functional brain regions. (b) Interpolated SHAP topographic map visualizing global feature attribution density. 4. Discussion The dominance of second-order scattering coefficients signifies schizophrenia as a dis… view at source ↗
read the original abstract

Schizophrenia is a debilitating neuropsychiatric disorder characterized by profound cortical network dysregulation, for which objective, clinically translatable EEG based biomarkers remain underdeveloped. Existing automated classification pipelines rely predominantly on static power spectral density features inherently blind to amplitude modulation dynamics and cross-frequency coupling, phenomena central to schizophrenia pathophysiology, while adopting epoch level cross validation strategies that introduce temporal data leakage, artificially inflate reported performance. This study introduces a mathematically principled diagnostic framework integrating the multi-order Wavelet Scattering Transform(WST), strict Leave One Subject Out (LOSO) cross-validation, and SHAP explainability for simultaneous EEG classification and biomarker discovery. Hierarchical WST coefficients capturing multi-scale amplitude modulation structure were extracted from resting state multichannel EEG. Subject-level ANOVA with Benjamini Hochberg false discovery rate correction identified significant biomarkers, with Random Forest and SVM classifiers evaluated under strict LOSO cross validation and subject-level majority voting. Second-order scattering coefficients encoding cross frequency coupling dominated the discriminative biomarker set, with gamma-band features most prevalent, demonstrating that temporal amplitude modulation constitutes the primary electrophysiological signature of schizophrenia. Electrode P3 was identified as the single most discriminative site. Under rigorous subject independent evaluation, the Random Forest achieved 90.48% accuracy (AUC = 0.9339; sensitivity = 95.56%). The proposed WST framework establishes a rigorous, interpretable standard for EEG-driven psychiatric biomarker discovery that can also be applicable in the detection of schizophrenia subtypes in the future.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 9 minor

Summary. This manuscript proposes a Wavelet Scattering Transform (WST) framework for schizophrenia biomarker discovery and classification from resting-state EEG. The pipeline extracts multi-order scattering coefficients (S0, S1, S2), applies subject-level ANOVA with FDR correction for biomarker identification, and trains Random Forest and SVM classifiers under strict Leave-One-Subject-Out (LOSO) cross-validation with subject-level majority voting. SHAP explainability analysis is used to cross-validate statistical biomarker findings. The RF classifier achieves 90.48% accuracy (AUC = 0.9339). The central biomarker claim is that second-order (S2) scattering coefficients, encoding cross-frequency coupling, dominate the discriminative feature set (78.5% of FDR-significant features), and that temporal amplitude modulation constitutes the primary electrophysiological signature of schizophrenia.

Significance. The manuscript addresses a genuine methodological gap in EEG-based schizophrenia classification by combining the WST (which captures amplitude modulation structure inaccessible to standard PSD features) with strict LOSO cross-validation and SHAP explainability. The use of subject-level statistics to avoid pseudo-replication from temporally overlapping epochs is a sound methodological choice. The LOSO evaluation protocol is appropriately rigorous for the 84-subject dataset. The reproducible use of kymatio for WST implementation and the publicly available Kaggle dataset are strengths. However, the central biomarker claim faces an internal consistency problem between the statistical analysis and the SHAP validation, as detailed below.

major comments (3)
  1. §1 (Introduction) and §3.5: The paper states that SHAP was incorporated 'to independently validate the identified biomarkers through cross-methodological consistency.' However, the SHAP results (§3.5) contradict the central biomarker claim rather than validating it. The top 5 SHAP-ranked features are all first-order (S1) coefficients (T5-S1[17], T6-S1[17], P3-S1[6], C4-S1[16], T6-S1[16]), while the paper's biomarker narrative rests on S2 dominance (78.5% of FDR-significant features). The Spearman correlation between F-score rankings and SHAP channel importance is ρs=0.429, p=0.0969 — non-significant. The paper frames this as 'moderate positive trend' and 'localized alignment,' but with p>0.05 this is a null result. Furthermore, the statistical analysis identifies P3 as the most discriminative electrode, while top SHAP features come from T5, T6, and C4. The claim of 'cross-methodological'
  2. §3.5 and §3.1: The spatial concordance claim is also inconsistent. The ANOVA identifies P3 as the single most discriminative electrode (12 of 27 Bonferroni-significant features), while SHAP channel-level importance (Fig. 11) shows P3, O1, and F4 as top regions. The paper states the model's decision architecture is 'primarily prioritized around the left-parietal (P3), left-occipital (O1), and right-frontal (F4) regions,' but the top individual SHAP features are from T5, T6, and C4. The authors should reconcile these discrepancies or temper the 'independent validation' framing. As written, the two methods disagree on both scattering order (S1 vs S2) and top electrode sites, which undermines the 'joint evidence' claim.
  3. Table 4: The proposed method's validation is listed as 'Subject-Level Holdout,' but the text (§2.6) describes Leave-One-Subject-Out cross-validation with 84 folds. These are different protocols. The table should say 'LOSO CV' to match the methodology. Additionally, the comparison with Sravanthi et al. (2026) [77], which uses 'Subject-wise LOOCV' on the same dataset (MHRC, 45 SZ / 39 HC) and reports 96.7% accuracy, is not discussed in the text despite being the most directly comparable result. The authors should comment on why their method underperforms this benchmark on the same data.
minor comments (9)
  1. §2.2: The specific z-score threshold value is not stated ('an adaptive z-score threshold was used'). The threshold is listed as a free parameter in the axiom ledger but its value should be reported for reproducibility.
  2. §2.6: The RF hyperparameters (200 trees, max depth 20) are stated but it is unclear whether these were selected via nested cross-validation or fixed a priori. If tuned on the same LOSO folds, this introduces optimistic bias. Please clarify the tuning protocol.
  3. §2.3: The claim that J=7 is 'the optimal choice' is supported by qualitative arguments about deformation stability and temporal dynamics, but no quantitative comparison with alternative J values is provided. Consider softening to 'a principled choice' rather than 'optimal,' or provide empirical justification.
  4. §3.1: The Bonferroni-significant subset (27 features) is described as comprising 'both first- and second-order scattering coefficients,' but the S1/S2 breakdown is not reported. Given that the FDR-significant set is 78.5% S2, the breakdown for the Bonferroni subset would be informative.
  5. §3.2: The statement 'no delta or theta features survived correction' is notable given the schizophrenia EEG literature's emphasis on slow-wave abnormalities. The authors attribute this to 'high cohort variability for slower alterations' but do not provide evidence. Consider softening this interpretation.
  6. Table 2: The 'Mean % Change' values appear to be computed from WST scattering coefficients, not raw spectral power. The table caption should clarify that these are percentage changes in scattering energy, not traditional band power.
  7. §4 (Discussion): Several references in the discussion (e.g., [61, 62, 63] cited together for posterior predominance) make it difficult to trace which specific finding from which citation supports which claim. Consider separating multi-citation clusters where they support distinct sub-claims.
  8. Fig. 10 caption: 'Fig' 10' has a stray apostrophe/quote mark. Should read 'Figure 10' or 'Fig. 10'.
  9. Abstract: 'Hierarchical WST coefficients capturing multi-scale amplitude modulation structure was extracted' — subject-verb agreement; should be 'were extracted.'

Simulated Author's Rebuttal

3 responses · 0 unresolved

WST-based EEG framework achieves 90.48% LOSO accuracy for schizophrenia classification; S2 coefficients dominate statistical biomarkers but SHAP prioritizes S1 features, creating an internal consistency problem requiring revision.

read point-by-point responses

  1. Referee: The SHAP results contradict the central biomarker claim: top 5 SHAP features are all S1, while the paper's narrative rests on S2 dominance. The Spearman correlation (ρs=0.429, p=0.0969) is non-significant, yet framed as 'moderate positive trend.' The claim of 'cross-methodological consistency' is not supported.

    Authors: The referee is correct that the current framing overstates the degree of cross-methodological consistency. We acknowledge the following: (1) The top-5 SHAP-ranked features are indeed all first-order (S1) coefficients, which contrasts with the S2 dominance (78.5%) observed in the FDR-significant biomarker set. (2) The Spearman correlation between F-score rankings and SHAP channel importance (ρs = 0.429, p = 0.0969) does not reach conventional statistical significance, and describing this as evidence of 'independent validation' is not justified. We will revise the manuscript to accurately characterize this as a null result for the rank correlation and to explicitly acknowledge the discrepancy in scattering order between the statistical and SHAP analyses. We believe this discrepancy is itself scientifically informative: univariate ANOVA identifies S2 features as the most statistically discriminative between groups, while the multivariate Random Forest model relies more heavily on S1 features for its classification decisions. This suggests that group-level statistical separation and model-level discriminative utility are related but distinct properties, and we will discuss this distinction explicitly rather than claiming validation. The 'independent validation' framing in the Introduction and §3.5 will be removed and replaced with a more measured characterization: SHAP provides complementary, model-level interpretability that partially overlaps with but does not replicate the statistical biomarker findings. We agree this is a substantive revision to the paper's narrative. revision: yes

  2. Referee: Spatial concordance claim is inconsistent: ANOVA identifies P3 as most discriminative electrode, while SHAP channel-level importance shows P3, O1, and F4 as top regions, and top individual SHAP features come from T5, T6, and C4. The two methods disagree on both scattering order and top electrode sites, undermining the 'joint evidence' claim.

    Authors: The referee correctly identifies a genuine inconsistency in our spatial concordance narrative. The discrepancy operates at two levels: (a) at the channel-aggregated level, P3 does appear prominently in both analyses (P3 is the most discriminative electrode in ANOVA and among the top three in SHAP channel-level importance), which represents partial spatial overlap; (b) at the individual feature level, the top SHAP features (T5-S1[17], T6-S1[17], C4-S1[16]) do not coincide with the top ANOVA features (dominated by P3). We will revise the manuscript to clearly separate these two levels of analysis and to state honestly that the spatial concordance is partial—limited to the channel-aggregated level for P3—rather than claiming broad 'joint evidence.' The discrepancy between channel-level SHAP importance (where P3, O1, F4 rank highly) and individual-feature-level SHAP importance (where T5, T6, C4 features top the list) likely reflects the fact that channel-level aggregation sums across many scattering paths, so a channel can rank highly without any single feature from it appearing in the top-5. We will add this explanation and remove the implication that the two methods converge on the same electrode sites at the feature level. The 'joint evidence' language will be removed. revision: yes

  3. Referee: Table 4 lists validation as 'Subject-Level Holdout' but the text describes LOSO CV with 84 folds. The table should say 'LOSO CV.' Additionally, the comparison with Sravanthi et al. (2026), which uses Subject-wise LOOCV on the same dataset and reports 96.7% accuracy, is not discussed despite being the most directly comparable result.

    Authors: The referee is correct on both points. First, the Table 4 label 'Subject-Level Holdout' is inaccurate; the methodology (§2.6) clearly describes 84-fold Leave-One-Subject-Out cross-validation. This is an error in the table and will be corrected to 'LOSO CV.' Second, we agree that the Sravanthi et al. (2026) result (96.7% accuracy on the same MHRC dataset with subject-wise LOOCV) is the most directly comparable benchmark and should be discussed explicitly. We will add a discussion paragraph addressing this comparison. We note the following relevant differences: Sravanthi et al. employ Variational Mode Decomposition with multi-domain features and evaluate 9 ML plus 7 optimized ML classifiers, selecting the best-performing configuration, whereas our approach uses a single Random Forest model on WST features. Their higher accuracy may reflect the broader feature space and classifier optimization strategy. However, we also note that our framework's primary contribution is not maximizing classification accuracy but rather the interpretable biomarker discovery pipeline (WST + ANOVA + SHAP), which provides neurophysiological insight that a VMD-based approach does not directly offer. We will state this comparison honestly, including the accuracy gap, rather than omitting it. revision: yes

Circularity Check

0 steps flagged

No significant circularity found; derivation chain is self-contained.

full rationale

The paper's derivation chain is straightforward and does not reduce to its inputs by construction. (1) WST coefficients are defined by standard wavelet mathematics (Eqs. 3–5, citing Mallat [28] and Bruna & Mallat [29] — external authors), independent of the schizophrenia data. (2) Biomarker identification uses subject-level ANOVA with BH-FDR correction on these pre-defined features — a standard statistical test, not a fit renamed as a prediction. (3) The RF classifier is trained on the full WST feature space under LOSO cross-validation; the SVM uses FDR-significant features but is a secondary classifier. Neither classifier's features are defined in terms of the labels. (4) SHAP analysis is applied post-hoc to the RF model using TreeExplainer (external method, Lundberg et al. [33]). No step is self-definitional, no parameter is fitted to a subset and then 'predicted' on closely related data, and no load-bearing self-citation chain exists — all key methods (WST, ANOVA, BH-FDR, LOSO, SHAP, TreeExplainer) are attributed to external sources. The paper's claim that 'S2 dominance proves amplitude modulation is the primary signature' is an inference from an empirical finding (78.5% of significant features are S2) combined with the mathematical definition of S2 (Eq. 5), which is not circular because the definition is independent of the data. The reader's concern about SHAP contradicting the ANOVA-based biomarker narrative (S1 vs S2 dominance, non-significant Spearman ρ=0.429, p=0.0969) is a legitimate correctness/overclaiming issue — the paper overstates 'cross-methodological consistency' — but it is not circularity: the SHAP analysis does not feed back into the ANOVA or feature definitions. Score 1 reflects the absence of circularity with a minor note that the 'independent validation' framing is overstated.

Axiom & Free-Parameter Ledger

5 free parameters · 1 axioms · 0 invented entities

string

free parameters (5)
  • J = 7
    string
  • Q = (8, 1)
    string
  • RF n_trees = 200
    string
  • RF max_depth = 20
    string
  • z-score threshold = not specified
    string
axioms (1)
  • domain assumption string
    string

pith-pipeline@v1.1.0-glm · 20054 in / 2587 out tokens · 49745 ms · 2026-07-07T19:46:35.609847+00:00 · methodology

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Reference graph

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