Horizontal Functional Principal Nested Spheres

Perform horizontal functional PCA using the principal nested spheres (fPNS) framework on warping functions. This captures the main modes of phase variability from the warping functions estimated during Karcher mean computation.

Usage

horiz.fpns(karcher, n.components = 3)

Arguments

karcher: An object of class 'karcher.mean' (result of karcher.mean).
n.components: Number of principal components to retain (default 3).

Value

A list with components:

scores: matrix of phase component scores (curves x components)
eigenvalues: numeric vector of eigenvalues
eigenfunctions: matrix of phase eigenfunctions (components x grid)
variance.explained: numeric vector of proportion of variance explained by each component

References

Jung, S., Dryden, I.L., and Marron, J.S. (2012). Analysis of principal nested spheres. Biometrika, 99(3):551–568.

Tucker, J.D., Wu, W., and Srivastava, A. (2013). Generative models for functional data using phase and amplitude separation. Computational Statistics & Data Analysis, 61:50–66.

Examples

# \donttest{
set.seed(1)
t <- seq(0, 1, length.out = 50)
X <- matrix(0, 20, 50)
for (i in 1:20) X[i, ] <- sin(2 * pi * t + runif(1, -0.3, 0.3))
fd <- fdata(X, argvals = t)
km <- karcher.mean(fd)
hfp <- horiz.fpns(km, n.components = 2)
# }