Fuzzy and Explainable AI for CMB Polarization Segmentation: Regional Stability Under Controlled Perturbations

This record corresponds to the accepted manuscript (post-print) of the following journal article:

“Fuzzy and Explainable AI for CMB Polarization Segmentation: Regional Stability Under Controlled Perturbations”

This article introduces a fuzzy and explainable artificial intelligence framework for the regional analysis of cosmic microwave background (CMB) polarization patterns. The proposed approach combines polarization-derived physical descriptors, Fuzzy C-Means clustering, supervised membership modeling, Explainable Artificial Intelligence (XAI), and controlled perturbation analysis to study the structure and stability of CMB polarization regions in an interpretable and reproducible way.

The methodology is applied to Planck SMICA CMB data. Starting from the Stokes polarization components Q and U, the polarization amplitude P and the scalar polarization modes E and B are derived. Regional features are then extracted over a HEALPix grid, considering only polarization-valid regions defined by the Planck polarization mask. Fuzzy clustering identifies four interpretable polarization regimes: high-polarization structured regions, E-dominated medium-polarization regions, B-enhanced medium-polarization regions, and low-polarization regions.

An XGBoost-SHAP layer is used to explain the resulting fuzzy memberships and to assess which physical descriptors contribute most to the regional polarization patterns. In addition, controlled perturbations are introduced into selected CMB-derived variables to evaluate how the fuzzy cluster structure changes under simulated disturbances. The results show a globally robust fuzzy structure with localized sensitivity, providing an interpretable methodology for studying regional CMB polarization patterns and their stability under controlled perturbations.

The final published version is available at the publisher’s website:

https://doi.org/10.3390/math14132269

This deposit is made for open access and dissemination purposes, in accordance with the publisher’s self-archiving policy.