This package contains a set of tools for performing functional independent component analysis (FICA) by analyzing the kurtosis structure of whitened data. Two FICA versions are considered depending on the basis of expansion: ffobi computes the independent components from a data representation in a canonical basis of functions, while kffobi uses the eigenfunctions of the covariance operator (in terms of basis functions). The application of penalties differs in both algorithms. The former introduces a penalty in the eigenfunctions of the kurtosis operator of a standardized sample; the latter in the eigenfunctions of the covariance operator for a subsequent standardization of the principal component expansion. This algorithm is also extended using a discrete penalty (P-spline) in pspline.kffobi, with this function being computationally more efficient. The current FICA routines use Mahalanobis kernel whitening and shrinkage covariance estimators to improve the outcomes in the estimation process. Our methods are interfaced with the basis systems provided in the fda package.
You can install the released version of pfica from CRAN with:
And the development version from GitHub with:
Vidal, M., M. Rosso and AM. Aguilera. (2021). Bi-Smoothed Functional Independent Component Analysis for EEG Artifact Removal. Mathematics 9(11) 1243. DOI: 10.3390/math9111243.