Sonification of the Cosmic Microwave Background: Interpretable Fuzzy Clustering for Multimodal Knowledge Extraction

Complex scientific datasets require interpretable machine-learning approaches capable of extracting structured information while preserving uncertainty and gradual transitions between data regimes. This work proposes an interpretable fuzzy clustering and sonification framework for the characterization and multimodal representation of Cosmic Microwave Background (CMB) data. Starting from Planck full-sky (I, Q, U) maps, the Stokes polarization parameters Q and U are processed to derive polarization amplitude, E- and B-mode components, and HEALPix-based regional descriptors, including mean polarization, polarization variability, E-mode energy, and the logarithmic B/E energy ratio. Fuzzy C-Means clustering identifies four interpretable regional regimes while preserving the complete membership vector of each region. Normalized fuzzy entropy characterizes membership dispersion and distinguishes clear, moderate, and ambiguous regions. The resulting physical and fuzzy representation is transformed into an auditory layer through explicit mappings between regional descriptors and sound parameters. Cluster-specific, global hard-label, global fuzzy, and entropy-based sonification outputs are evaluated using waveform, spectrogram, and spectral descriptors. Results reveal measurable spectral differences across the identified regimes and distinct spectral organizations between direct regional and membership-weighted synthesis. Overall, the framework provides a reproducible multimodal approach for uncertainty-aware characterization and exploratory analysis of complex scientific data.