Learning Locality-Aware Basis Functions via Spline-Wavelet Kolmogorov-Arnold Networks for Functional Data Classification

Functional data analysis (FDA) is widely used to model continuous processes from discrete observations across scientific domains. However, conventional FDA methods often rely on fixed basis families, leading to inefficient representations when discriminative patterns are concentrated within localized regions. To address this limitation, this work proposes Spline-Wavelet KAN for Adaptive Basis Learning (SKAB), a neural method that learns locality-aware basis functions for functional data classification. Motivated by an observed structural correspondence between FDA and Kolmogorov-Arnold Networks (KANs), SKAB formulates a KAN as a Coordinate-to-Basis Generator CBG that maps each functional-domain coordinate to basis functions. To better capture localized patterns, Spline-Wavelet KAN is introduced to parameterize the CBG using compactly supported B-spline wavelet atoms as edge functions. Each functional observation is projected onto the learned bases to obtain a coefficient representation for downstream prediction. Experiments on synthetic and real-world datasets demonstrate that SKAB achieves competitive classification performance, with particular advantages for data containing localized discriminative patterns. The code is available at this link.