optimum.reparam {fdasrvf}

Align two functions

Description

This function aligns the SRVFs of two functions in R^1 defined on an interval [t_{\min}, t_{\max}] using dynamic programming or RBFGS

Usage

optimum.reparam(
  Q1,
  T1,
  Q2,
  T2,
  lambda = 0,
  pen = "roughness",
  method = c("DP", "DPo", "SIMUL", "RBFGS"),
  f1o = 0,
  f2o = 0,
  nbhd_dim = 7
)

Arguments

Q1

A numeric matrix of shape ⁠n_points x n_dimensions⁠ specifying the SRSF of the 1st n_dimensions-dimensional function evaluated on a grid of size n_points of its univariate domain.

T1

A numeric vector of size n_points specifying the grid on which the 1st SRSF is evaluated.

Q2

A numeric matrix of shape ⁠n_points x n_dimensions⁠ specifying the SRSF of the 2nd n_dimensions-dimensional function evaluated on a grid of size n_points of its univariate domain.

T2

A numeric vector of size n_points specifying the grid on which the 1st SRSF is evaluated.

lambda

A numeric value specifying the amount of warping. Defaults to 0.0.

pen

alignment penalty (default="roughness") options are second derivative ("roughness"), geodesic distance from id ("geodesic"), and norm from id ("l2gam"), srvf norm from id ("l2psi")

method

A string specifying the optimization method. Choices are "DP", "DPo", "SIMUL", or "RBFGS". Defaults to "DP".

f1o

A numeric vector of size n_dimensions specifying the value of the 1st function at t = t_{\min}. Defaults to rep(0, n_dimensions).

f2o

A numeric vector of size n_dimensions specifying the value of the 2nd function at t = t_{\min}. Defaults to rep(0, n_dimensions).

nbhd_dim

size of the grid (default = 7)

Value

A numeric vector of size n_points storing discrete evaluations of the estimated boundary-preserving warping diffeomorphism on the initial grid.

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 functional data using phase and amplitude separation, Computational Statistics and Data Analysis (2012), 10.1016/j.csda.2012.12.001.

Examples

q <- f_to_srvf(simu_data$f, simu_data$time)
gam <- optimum.reparam(q[, 1], simu_data$time, q[, 2], simu_data$time)