A Quadratic Discriminant Analysis Rule for Spatial Functional Data: Application to EEG Data for Silent Speech Recognition

This paper introduces a novel version of the quadratic discriminant analysis rule for spatial functional data, based on the Mahalanobis distance for spatially correlated functional data. This approach is relevant when the differences among the groups are not only in the mean function but also in the covariance structure. We estimate the mean function and a valid model for the covariance structure of each group and perform discriminant analysis for spatial functional data. Our proposal is inspired by brain signals from the language area, although not limited to this field. The accurate discriminant analysis of silent vowels obtained through electroencephalography (EEG) signals holds great potential to enhance communication in individuals. EEG signals represent curves measured at a finite number of locations in the brain, and can be treated as spatial functional data, allowing for a comprehensive analysis of their spatial characteristics. The methodology is applied to a dataset of EEG brain signals of people while they were thinking about each of the five vowels of the Spanish language in a silent voice. An additional application to climate data, and a simulation study to evaluate the performance, are included.