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Mathematics
Article . 2026 . Peer-reviewed
License: CC BY
Data sources: Crossref
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Fuzzy and Explainable AI for CMB Polarization Segmentation: Regional Stability Under Controlled Perturbations

Authors: Gabriel Marín Díaz;

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

Abstract

The cosmic microwave background (CMB) contains key information about the early Universe, particularly through its polarization structure. This work proposes a Fuzzy and Explainable Artificial Intelligence framework (FAS-XAI) for the regional analysis of CMB polarization using Planck SMICA data. From the Stokes 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 C-Means 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. XGBoost accurately reproduces the memberships, with R2 > 0.98 for all clusters, while SHAP confirms the physical relevance of amplitude-related features and the log(B/E) balance. Finally, controlled perturbations in P and log(B/E) reveal a globally robust fuzzy structure with localized sensitivity. The proposed framework provides an interpretable methodology for studying regional CMB polarization patterns and their stability under controlled perturbations.

Keywords

cosmic microwave background, Fuzzy C-Means, SHAP, HEALPix, CMB polarization, perturbation analysis, explainable AI

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
0
Average
Average
Average