In this paper, we introduce classification of complex high dimensional functional data in the functional mixed model (FMM) framework. The FMM relates a functional response to a set of scalar predictors through functional fixed and random effects, and therefore is able to account for various factors that affecting the functions and inducing correlations. Classification is performed through training the data by treating the class as one of the fixed effects, and then predicting on the test data using posterior predictive probabilities. Through a Bayesian scheme, we are able to incorporate not only all factors that influencing the functions, but also factors that directly affect class designation. While this classification method is general for all FMM methods, 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 accommodates various nonstationarities. The R-WFMM has the additional advantage of allowing 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 real mass spectroscopy dataset in pancreatic cancer research. Our results show improved classification when comparing FMM with other typical functional data classification methods and the ad hoc methods that are based on detected spectral peaks.
Statistical Methodology | Statistical Models | Statistical Theory
Zhu, Hongxiao; Brown, Philip J.; and Morris, Jeffrey S., "Robust Classification of Functional and Quantitative Image Data using Functional Mixed Models" (July 2011). UT MD Anderson Cancer Center Department of Biostatistics Working Paper Series. Working Paper 72.