jointFPCAh: Joint Vertical and Horizontal Functional Principal Component Analysis

Description

This function calculates amplitude and phase joint functional principal component analysis on aligned data using the SRVF framework using MFPCA and h representation

Usage

jointFPCAh(
  warp_data,
  var_exp = 0.99,
  id = round(length(warp_data$time)/2),
  C = NULL,
  ci = c(-1, 0, 1),
  srvf = TRUE,
  showplot = TRUE
)

Value

Returns a list containing

q_pca: srvf principal directions
f_pca: f principal directions
latent: latent values
coef: coefficients
U: eigenvectors
mu_psi: mean psi function
mu_g: mean g function
id: point use for f(0)
C: optimized phase amplitude ratio

Arguments

warp_data: fdawarp object from time_warping of aligned data
var_exp: compute no based on value percent variance explained (default: 0.99) will override no
id: integration point for f0 (default = midpoint)
C: balance value (default = NULL)
ci: geodesic standard deviations (default = c(-1,0,1))
srvf: use srvf (default = TRUE)
showplot: show plots of principal directions (default = T)

References

Srivastava, A., Wu, W., Kurtek, S., Klassen, E., Marron, J. S., May 2011. Registration of functional data using fisher-rao metric, arXiv:1103.3817v2.

Happ, C., Scheipl, F., Gabriel, A. & Greven, S. A general framework for multivariate functional principal component analysis of amplitude and phase variation. Stat 8, (2019).

Ma, Y., Zhou, X. & Wu, W. A stochastic process representation for time warping functions. Comput. Stat. Data Anal. 194, 107941 (2024).

Tucker, J. D., Wu, W., Srivastava, A., Generative Models for Function Data using Phase and Amplitude Separation, Computational Statistics and Data Analysis (2012), 10.1016/j.csda.2012.12.001.

Examples

Run this code

jfpcah <- jointFPCAh(simu_warp)

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