Mixtures of spatial spline regressions for clustering and classification

Classification and clustering of functional data arise in many areas of modern research. Currently, techniques for performing such tasks have concentrated on applications to univariate functions. Such techniques can be extended to the domain of classifying and clustering bivariate functions (i.e. surfaces) over rectangular domains. This is achieved by combining the current techniques in spatial spline regression (SSR) with finite mixture models and mixed-effects models. As a result, three novel techniques have been developed: spatial spline mixed models (SSMM) for fitting populations of surfaces, mixtures of SSR (MSSR) for clustering surfaces, and MSSR discriminant analysis (MSSRDA) for classification of surfaces. Through simulations and applications to problems in handwritten character recognition, it is shown that SSMM, MSSR, and MSSRDA are effective in performing their desired tasks. It is also shown that in the context of handwritten character recognition, MSSR and MSSRDA are comparable to established methods, and are able to outperform competing approaches in missing-data situations.