This is an internal function of package FRTM which allows controlling the parameters to implement the OEB-FDTW in the FRTM method.
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)
)The number \(N_{t}\) of evenly spaced values along the template domain \(\mathcal{D}_{Y}\).
The number \(M_{x}\) of evenly spaced values along the functional observation domain \(\mathcal{D}_{X_i}\).
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.
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.
Grid of values to find the optimal value of \(\alpha_i\).
Fraction of \(\mathcal{D}_{Y}\) and \(\mathcal{D}_{X_i}\) to obtain \(\delta_{t,s}\), \(\delta_{t,e}\),\(\delta_{x,s}\) and \(\delta_{x,e}\).
Fraction \(\eta\) for updating the constraint bounds to reduce the error associated to the discretization (Deriso and Boyd, 2022).
Number of iteration in the iterative refinement to reduce the error associated to the discretization (Deriso and Boyd, 2022).
If "Procrustes", the Procrustes fitting process is used to select the template function. If numeric, the discrete observations of the template function.
If template is numeric, a vector of time points where the discrete observations of the template function are sampled.
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.
Number of iterations in the Procrustes fitting process.
Grid of smoothing parameters to evaluate the average curve distance (ACD).
The fraction \(\delta\) of the difference between the maximum and the minimum distance in the selection of the smoothing parameter via the ACD.
Discretized sequence in the template domain \(\mathcal{D}_{Y}\).
F. Centofanti
Deriso, D. and S. Boyd (2022). A general optimization framework for dynamic time warping. Optimization and Engineering, 1-22.
FRTM_PhaseI