gcv function

Generalized cross-validation for the FCP-TPA algorithm

These function calculates the generalized cross-validation criterion for the smoothing parameters $\alpha_v$ or $\alpha_w$ 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.

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.

Returns

The value of the GCV criterion.

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!

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