par.FDTW: Setting open-end/open-begin functional dynamic time warping...
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par.FDTW

R Documentation

Setting open-end/open-begin functional dynamic time warping (OEB-FDTW) defaults

Description

This is an internal function of package FRTM which allows controlling the parameters to implement the OEB-FDTW in the FRTM method.

Usage

par.FDTW(
  N = 100,
  M = 50,
  smin = NULL,
  smax = NULL,
  alpha_vec = c(0, 0.5, 1),
  frac_oeob = 0.1,
  eta = 0.5,
  iter = 3,
  template = "Procrustes",
  grid_tem = NULL,
  index_tem = NULL,
  iter_tem = 2,
  lambda = c(0, 10^seq(-8, -2, by = 0.25), 10^5),
  threshold = 0.01,
  seq_t = seq(0.01, 1, length.out = 100)
)

Arguments

`N`	The number `N_{t}` of evenly spaced values along the template domain `\mathcal{D}_{Y}`.
`M`	The number `M_{x}` of evenly spaced values along the functional observation domain `\mathcal{D}_{X_i}`.
`smin`	The minimum values allowed for the first derivative of the warping function `h_i`. If NULL, in `FRTM_PhaseI`, it is set as 0.001 multiplied by the ratio between the size of the monitoring and template domains.
`smax`	The maximum values allowed for the first derivative of the warping function `h_i`. If NULL, in `FRTM_PhaseI`, it is set as 100 multiplied by the ratio between the size of the monitoring and template domains.
`alpha_vec`	Grid of values to find the optimal value of `\alpha_i`.
`frac_oeob`	Fraction of `\mathcal{D}_{Y}` and `\mathcal{D}_{X_i}` to obtain `\delta_{t,s}`, `\delta_{t,e}`,`\delta_{x,s}` and `\delta_{x,e}`.
`eta`	Fraction `\eta` for updating the constraint bounds to reduce the error associated to the discretization (Deriso and Boyd, 2022).
`iter`	Number of iteration in the iterative refinement to reduce the error associated to the discretization (Deriso and Boyd, 2022).
`template`	If "Procrustes", the Procrustes fitting process is used to select the template function. If `numeric`, the discrete observations of the template function.
`grid_tem`	If `template` is `numeric`, a vector of time points where the discrete observations of the template function are sampled.
`index_tem`	If NULL and `template="Procrustes"`, the function in the training set, whose domain length is nearest the median domain length, is chosen as initial estimate of the template function. If an `integer` and `template="Procrustes"`, the `index_tem` function in the training set is chosen as initial estimate of the template function. If `template` is `numeric`, this parameter is not used.
`iter_tem`	Number of iterations in the Procrustes fitting process.
`lambda`	Grid of smoothing parameters to evaluate the average curve distance (ACD).
`threshold`	The fraction `\delta` of the difference between the maximum and the minimum distance in the selection of the smoothing parameter via the ACD.
`seq_t`	Discretized sequence in the template domain `\mathcal{D}_{Y}`.