NIR and mass spectra classification: Bayesian methods for wavelet-based feature selection

Here we focus on classification problems that involve functional predictors, specifically spectral data. One of our practical contexts involves the classification of three wheat varieties based on 100 near infra-red absorbances. The dataset consists of a total 117 samples of wheat collected during a study that aimed at exploring the possibility of using NIR spectra to assign unknown samples to the correct variety. In another example we look at serum spectra from 162 ovarian cancer and 91 control subjects generated through surface enhanced laser desorption ionization time-to-flight mass spectrometry (SELDI-TOF). We employ wavelet transforms as a tool for dimension reduction and noise removal, reducing spectra to wavelet components. We then use probit models and Bayesian methods that allow the simultaneous classification of the samples as well as the selection of the discriminating features of the spectra. In both examples our method is able to find very small sets of features that lead to good classification results.