Beta Wavelet Induced Multi-Scale Kernel Clustering: A Frequency-Aware Framework for Complex Data Analysis

Conventional multi-kernel clustering methods typically focus on selecting diverse kernel functions in the original feature space while overlooking the structural information embedded in different frequency components. This limits their ability to handle complex data distributions, especially with multi-scale patterns and noise. To address this, we propose a novel clustering paradigm that leverages Beta wavelet transforms to construct frequency-aware kernel representations. By systematically decomposing single-view data into multiple frequency components, our method enriches the feature space with hierarchical spectral information. Beta wavelet filtering generates transformed representations that emphasize distinct frequency characteristics, capturing both local and global structures. A multi-kernel fusion strategy integrates these representations, preserving scale-specific similarities while maintaining cross-frequency coherence. Experiments on benchmark datasets demonstrate notable improvements in clustering accuracy, validating the benefit of incorporating frequency-domain insights into multi-kernel clustering. This work introduces a new perspective on unsupervised learning, highlighting spectral decomposition as a key step for robust and interpretable clustering. Code is available at https://github.com/Lwhite111/BWMSKC.