WITHDRAWN Multidimensional Functional Data Analysis Using Marginal Product Basis System

Music City Center 

Advances in data storage and sensor technology have led to a surge in multidimensional functional datasets across fields like neuroimaging and climate science. A common analytic approach involves first mapping discrete observations into continuous functional representations, followed by statistical analysis on the smoothed functions. However, traditional one-dimensional (univariate) functional data analysis approaches struggle with the curse of dimensionality when extended to multidimensional domains. We propose a computational framework for learning continuous representations of multidimensional functional data that overcomes these challenges. Our method constructs representations using data-adaptive separable basis functions and efficiently estimates them via tensor decomposition of a transformed data structure. We further incorporate roughness-based regularization through differential operator-based penalties. In this presentation, we discuss key theoretical properties of our approach and provide extensive simulation studies showcasing its advantages over existing methods.

multidimensional functional data analysis

tensor decomposition

basis representation

functional principal component analysis

brain image analysis 

International Chinese Statistical Association