Mixtures of Spatial Spline Regressions
Abstract
We present an extension of the functional data analysis framework for univariate functions to the analysis of surfaces: functions of two variables. The spatial spline regression (SSR) approach developed can be used to model surfaces that are sampled over a rectangular domain. Furthermore, combining SSR with linear mixed effects models (LMM) allows for the analysis of populations of surfaces, and combining the joint SSR-LMM method with finite mixture models allows for the analysis of populations of surfaces with sub-family structures. Through the mixtures of spatial splines regressions (MSSR) approach developed, we present methodologies for clustering surfaces into sub-families, and for performing surface-based discriminant analysis. The effectiveness of our methodologies, as well as the modeling capabilities of the SSR model are assessed through an application to handwritten character recognition.
Keywords
Cite
@article{arxiv.1306.3014,
title = {Mixtures of Spatial Spline Regressions},
author = {Hien D. Nguyen and Geoffrey J. McLachlan and Ian A. Wood},
journal= {arXiv preprint arXiv:1306.3014},
year = {2013}
}