fdasrvf (version 2.3.6)

pair_align_functions: Align two functions

Description

This function aligns two functions using SRSF framework. It will align f2 to f1

Usage

pair_align_functions(
  f1,
  f2,
  time,
  lambda = 0,
  pen = "roughness",
  method = "DP",
  w = 0.01,
  iter = 2000
)

Value

Returns a list containing

f2tilde

aligned f2

gam

warping function

Arguments

f1

function 1

f2

function 2

time

sample points of functions

lambda

controls amount of warping (default = 0)

pen

alignment penalty (default="roughness") options are second derivative ("roughness"), geodesic distance from id ("geodesic"), and norm from id ("norm")

method

controls which optimization method (default="DP") options are Dynamic Programming ("DP"), Coordinate Descent ("DP2"), Riemannian BFGS ("RBFGS"), Simultaneous Alignment ("SIMUL"), Dirichlet Bayesian ("dBayes"), and Expo-Map Bayesian ("expBayes")

w

controls LRBFGS (default = 0.01)

iter

number of mcmc iterations for mcmc method (default 2000)

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.

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.

Cheng, W., Dryden, I. L., and Huang, X. (2016). Bayesian registration of functions and curves. Bayesian Analysis, 11(2), 447-475.

Lu, Y., Herbei, R., and Kurtek, S. (2017). Bayesian registration of functions with a Gaussian process prior. Journal of Computational and Graphical Statistics, DOI: 10.1080/10618600.2017.1336444.

Examples

out <- pair_align_functions(
  f1 = simu_data$f[, 1],
  f2 = simu_data$f[, 2],
  time = simu_data$time
)