A1618
Title: Flexible functional data representation in higher dimensions using state space transformation
Authors: Hiba Nassar - Technical University of Denmark (Denmark) [presenting]
Abstract: Functional data analysis (FDA) traditionally involves two steps: representing discrete observations as continuous functions and then applying functional methods to the represented data. The choice of the initial functional basis can significantly impact the outcomes of subsequent analyses. Recent research has demonstrated that data-driven spline bases can outperform predefined, rigid representations by using efficient knot placement through machine learning algorithms. However, extending these methods to higher-dimensional domains, such as images, presents challenges. The use of tensor-based spline spaces in such contexts requires knots to be placed on a lattice, which restricts the flexibility of knot placement, an essential aspect of effective modeling. A novel approach is introduced based on state space transformation, which accounts for the distribution of knots not through the direct construction of spline bases but by embedding knot selection into the underlying structure of the transformation. This method offers a more flexible and adaptable functional representation for higher-dimensional data. Preliminary results suggest this approach significantly enhances the ability to model complex data domains, particularly those with image-like structures.
