Validation-Aware Retrospective EEG Treatment-Response Modelling Using Chaotic Pattern of Prime Numbers Features: Segment-Level Separability and Subject-Wise Generalisation

Overview

1. Department of Information Science, University of North Texas, Denton, TX 76203, USA; (H.A.); (M.M.)
2. Department of Psychiatry, University of Tehran, Tehran 141556619, Iran; (R.R.); (R.K.)
3. School of Computer Science and Electronic Engineering, University of Essex, Colchester CO4 3SQ, UK

Abstract

This study presents a validation-aware EEG framework based on Chaotic Pattern of Prime Numbers (CPPN) features for depression treatment-response modelling across one SSRI cohort and two rTMS cohorts. CPPN features were evaluated through a seven-protocol validation hierarchy spanning random segment splitting, segment-level cross-validation, nested segment-level cross-validation, leave-N-subjects-out, fixed-feature leave-one-subject-out (LOSO), nested leave-N-subjects-out, and nested LOSO, with normalisation, NCA ranking, feature-count selection where applicable, and model fitting confined to the appropriate training partitions. In the representative K-nearest neighbour (KNN) comparison, segment-level 10-fold CV achieved accuracies of 98.79% for Mumtaz SSRI, 99.32% for small Atieh rTMS, and 99.42% for big Atieh rTMS, demonstrating strong discriminative structure in the CPPN feature space. In the available segment-level KNN comparison, CPPN features with fold-internal NCA-selected feature sets exceeded conventional statistical EEG features by 29.53, 16.33, and 11.45 percentage points across the three cohorts. Subject-wise validation produced lower and more cohort-dependent estimates, with the best fixed-feature LOSO accuracy of 80.00% and the best nested LOSO accuracy of 73.33% in the small Atieh rTMS cohort. These results show that CPPN provides a compact, inspectable and computationally accessible EEG feature representation, while the validation hierarchy gives a transparent account of how performance changes from segment-level separability to held-out-subject evaluation. The main contribution is methodological: this study combines an original CPPN feature representation with explicit validation-depth analysis, leakage-aware feature selection, and interpretable channel/bin inspection. It therefore provides a rigorous basis for future externally validated EEG treatment-response studies without claiming prospective clinical deployment from the present retrospective cohorts.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Data

Datasets cited

• figshare:2 — at figshare; found in the references
• figshare:4244171 — at figshare; found in “Data Availability Statement”

Data Availability Statement

The Mumtaz SSRI dataset analysed in this study is publicly available from the source described in the original dataset publication [10,24] and through Figshare at https://doi.org/10.6084/m9.figshare.4244171.v2. The Atieh Hospital rTMS datasets are not publicly available because they contain clinical participant data and are subject to institutional and ethical restrictions. Requests for access to the private rTMS data and derived analysis materials may be directed to the corresponding author and will be considered subject to internal approval, institutional data-governance requirements, and participant-confidentiality restrictions where appropriate. Derived CPPN feature matrices, class labels, and analysis scripts may be made available by the corresponding author upon reasonable request, subject to institutional approvals and applicable data-governance restrictions.

Reproduced under the paper's license (CC BY), from the paper cited above.

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 5 authors, 14 keywords, 29 references.

Cite

This paper

Akbari, H., Mete, M., Rostami, R., Kazemi, R., & Sadiq, M. T. (2026). Validation-Aware Retrospective EEG Treatment-Response Modelling Using Chaotic Pattern of Prime Numbers Features: Segment-Level Separability and Subject-Wise Generalisation. Bioengineering (Basel, Switzerland), 13(6), 659.

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