pfica:: Performs penalized (and non-penalized) independent component analysis for univariate functional data. Two alternative versions are implemented, both based on the spectral decomposition of the kurtosis operator. Our methods are interfaced with the basis systems provided in the fda package.
Marc Vidal marc.vidalbadia@ugent.be, Ana Mª Aguilera aaguiler@ugr.es
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.
Ramsay, J. and B. Silverman (2005). Functional Data Analysis. Springer.
Schafer, J. and K. Strimmer (2005). A shrinkage approach to large-scale covariance matrix estimation and implications for functional genomics. Statistical Applications in Genetics and Molecular Biology, 4.32(1).
Vidal, M., M. Rosso and AM. Aguilera. (2021). Bi-Smoothed Functional Independent Component Analysis for EEG Artifact Removal. Mathematics 9(11) 1243.
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