The Functional Regression With Reconstructed Functions From Hybrid Principal Components Analysis: With EEG-fMRI Application

Abstract

Objective: In this article, we reconstruct the hybrid data with hybrid principal component analysis (HPCA) as a feature extraction step and model them with functional regression as a modeling step, and comparing models and choose the best number of HPCA based on the prediction accuracy as an evaluation step. Method: We decompose the hybrid data to the eigencomponents with HPCA. The reconstructed data from HPCA were divided into the training and testing dataset. The function-on-function signal compression and scalar-on-function regressions were used. Three simulation scenarios and their applications in the neuroimaging datasets (EEG-fMRI) were studied. The number of HPCA was selected with the mean squared prediction error (MSPE). Result: The simulation shows that the raw data, reconstructed from the first and all HPCAs for the training dataset has median MSPE 0.1001, 0.0028, and 0.0174 respectively, and for the testing, the dataset has 0.3207, 0.1118, and 0.2484 respectively. The EEG-fMRI suggests that in both auditory and visual tasks and standard and target stimuli for different regions of the brain the first HPCA has the smallest MSPE. Conclusions: We conclude this method improves the prediction accuracy of the experiments with the EEG datasets. And we recommend that instead of using the functional PCA on the desired dimension, reconstruct the data with HPCA and average it on the other two dimensions for functional regression models.