This function calculates the kurtosis distance (Vidal, 2020), which is an ad-hoc measure to select the number of components to be computed in kffobi and pspline.kffobi.
kd(fdx, hm = fdPar(fdx), pp = NULL, r = 2,
pr = c("fdx", "fdx.st", "KL", "KL.st"),
centerfd = FALSE, qmin = 2, qmax = 5)A vector of kurtosis distance values.
a functional data object obtained from the fda package.
a functional parameter object, obtained from the fda package, that defines the independent component functions to be estimated in kffobi.
the penalty parameter to perform kd on pspline.kffobi.
a number indicating the order of the penalty to perform kd on pspline.kffobi
.
the functional data object to project into the space spanned by the eigenfunctions of the kurtosis operator. To compute the independent components, the usual procedure is to use KL.st, the standardized principal component expansion. Thus, if pr is not supplied, KL.st is used.
a logical value indicating whether the mean function has to be subtracted from each functional observation.
the minimum allowable \(q\) degree.
the maximum allowable \(q\) degree.
Marc Vidal
The kurtosis distance measures the degree of extremeness in a component space by computing the excess kurtosis on each score vector and the distance between the most extreme kurtosis values using the Frobenius norm.
Vidal, M. (2020). Functional Independent Component Analysis in Bioelectrical Signal Processing. MA thesis. Universidad de Granada.
kffobi