Mixtures of Spatial Spline Regressions

TL;DR

This paper extends functional data analysis to surfaces using spatial spline regressions, enabling modeling, clustering, and discriminant analysis of surface data, demonstrated through handwritten character recognition.

Contribution

It introduces mixtures of spatial spline regressions (MSSR), combining SSR, LMM, and finite mixture models for surface clustering and analysis, a novel methodological integration.

Findings

Effective surface clustering demonstrated on handwritten characters

SSR model successfully captures surface variations

Methodology outperforms existing approaches in surface analysis

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.