Calendar – Econometrics and Statistics

Title : Functional additive models for forms of plane curves and their visualization:

Abstract : In many imaging data problems, the coordinate system of recorded objects is arbitrary or explicitly not of interest. Statistical shape analysis addresses this by identifying the object of analysis as the "shape" of observation, i.e., its equivalence class modulo translation, rotation and re-scaling, or as its "form" modulo translation and rotation. A flexible additive regression framework is introduced for modeling the shape or form of planar (potentially irregularly sampled) curves and/or landmark configurations in dependence on scalar covariates. The focus is on an analysis of the form of cell outlines generated from a cellular Potts model in dependence on different metric biophysical model parameter effects (including smooth interactions). Graphic illustration usually plays an essential role in the practical interpretation of smooth (non-linear) additive model effects but becomes a challenging task when the response presents an (equivalence class of) planar curves or landmark configurations. Therefore, a novel visualization for multidimensional functional regression models is also suggested. Analogous to principal component analysis often used for the visualization of functional data, a suitable tensor-product factorization decomposes each covariate effect. After decomposition, the main effect directions can be illustrated on the level of curves, while the effect into the respective direction is visualized by standard effect plots for scalar additive models.