A0902
Title: Composite basis expansions for unified functional representation of high-dimensional multilevel spatiotemporal data
Authors: Yuko Araki - Tohoku University (Japan) [presenting]
Abstract: A novel composite basis expansion method is proposed for the functional representation of high-dimensional spatiotemporal data characterized by heterogeneous observation times, individual-level variation, and multilevel structure. The method aims to minimize information loss while maintaining a unified modeling framework. Traditional functional data analysis often employs principal components or Wavelet bases, assuming regular observation grids and low noise. However, real-world datasets in domains such as medical imaging and physiological monitoring commonly violate these assumptions, presenting irregular sampling densities and small sample sizes. These features challenge the stability and flexibility of conventional functionalization approaches. To address these limitations, a composite basis is constructed that integrates elements from multiple basis construction strategies, including sparse singular value decomposition and a form of dynamic mode decomposition. This framework enables the smooth and robust functional representation of structurally complex data. In addition, a novel information criterion tailored to functional spaces is proposed, designed to guide the selection of basis dimensionality in a way that mitigates overfitting while maximizing information retention.
