fdasrvf (version 2.5.0)

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"), \(L^2\) distance of the warping function from id ("l2gam"), \(L^2\) distance of the SRVF of the warping function from that of id ("l2psi"), geodesic distance from id ("geodesic"), and no penalty ("none"). "norm" is kept for backward compatibility as an alias for "l2gam". The penalty is weighted by lambda, so it has no effect when lambda = 0.

method

controls which optimization method (default="DP") options are Dynamic Programming ("DP"), the original Dynamic Programming implementation ("DPo"), 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
)