Classification of Signals Using Wavelets and Principal Components Reduction, with Application to Auditory Brain Activity

The paper deals with a generalized linear model with functional data using a wavelet representation of the signals. A reduction of dimension is first obtained through a principal component analysis. The discriminative function is then given by a loglikelihood maximization, with a LASSO penalization, in order to ensure the sparsity of the wavelet representation. In order to have a data-driven procedure, we explore different cross-validation schemes. A simulation study is presented, showing our estimator that is competitive with those described in Reiss and Ogden (2013). We apply this model to a classification of functional EEG data, to study the capacity of discrimination of nearby sounds.