Robust Classification of Functional and Quantitative Image Data Using Functional Mixed Models

This paper describes how to perform classification of complex, high-dimensional functional data using the functional mixed model (FMM) framework. The FMM relates a functional response to a set of predictors through functional fixed and random effects, which allows it to account for various factors and between-function correlations. Classification is performed through training the model treating class as one of the fixed effects, and then predicting on the test data using posterior predictive probabilities of class. Through a Bayesian scheme, we are able to adjust for factors affecting both the functions and the class designations. While the method we present can be applied to any FMM-based method, we provide details for two specific Bayesian approaches: the Gaussian, wavelet-based functional mixed model (G-WFMM) and the robust, wavelet-based functional mixed model (R-WFMM). Both methods perform modeling in the wavelet space, which yields parsimonious representations for the functions, and can naturally adapt to local features and complex nonstationarities in the functions. The R-WFMM allows potentially heavier tails for features of the functions indexed by particular wavelet coefficients, leading to a down weighting of outliers that makes the method robust to outlying functions or regions of functions. The models are applied to a pancreatic cancer mass spectroscopy data set and compared with some other recently developed functional classification methods.