gcv: Generalized cross-validation for the FCP-TPA algorithm

In MFPCA: Multivariate Functional Principal Component Analysis for Data Observed on Different Dimensional Domains

Generalized cross-validation for the FCP-TPA algorithm

Description

These function calculates the generalized cross-validation criterion for the smoothing parameters α_v or α_w that are used in the FCP_TPA algorithm. As the criterion is symmetric in v and w, this function implements a generic criterion, which is called by findAlphaVopt, findAlphaWopt with the correct values.

Usage

gcv(alpha, n, z, eta, lambda)

Arguments

alpha	The current value of the smoothing parameter.
n	The length of the dimension, for which the smoothing parameter is to be optimized.
z	A vector of length n. See Details.
eta	A vector of length n. See Details.
lambda	A vector of length n, containing the eigenvalues of the penalty matrix corresponding the the current image direction.

Details

The criterion can be evaluated in a numerically efficient way, adopting the ideas in Huang, Shen and Buja (2008) to three-ways tensors. TODO!

Value

The value of the GCV criterion.

References

G. I. Allen, "Multi-way Functional Principal Components Analysis", IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing, 2013.

See Also

FCP_TPA

MFPCA documentation built on Sept. 15, 2022, 9:07 a.m.