loss_h_gradient {registr}

Gradient of loss function for registration step

Description

Gradient of loss function for registration step

Usage

loss_h_gradient(
  Y,
  Theta_h,
  mean_coefs,
  knots,
  beta.inner,
  family = "gaussian",
  incompleteness = NULL,
  lambda_inc = NULL,
  t_min,
  t_max,
  t_min_curve,
  t_max_curve,
  Kt = 8,
  periodic = FALSE,
  warping = "nonparametric"
)

Arguments

Y

vector of observed points.

Theta_h

B-spline basis for inverse warping functions.

mean_coefs

spline coefficient vector for mean curve.

knots

knot locations for B-spline basis used to estimate mean and FPC basis function.

beta.inner

spline coefficient vector to be estimated for warping function h.

family

One of c("gaussian","binomial"). Defaults to "gaussian".

incompleteness

Optional specification of incompleteness structure. One of c("leading","trailing","full"), specifying that incompleteness is present only in the initial measurements, only in the trailing measurements, or in both, respectively. For details see the accompanying vignette. Defaults to NULL, i.e. no incompleteness structure. Can only be set when warping = "nonparametric".

lambda_inc

Penalization parameter to control the amount of overall dilation of the domain. The higher this lambda, the more the registered domains are forced to have the same length as the observed domains. Only used if incompleteness is not NULL.

t_min

minimum and maximum value to be evaluated on the time domain.

t_max

minimum and maximum value to be evaluated on the time domain.

t_min_curve

minimum and maximum value of the observed time domain of the (potentially incomplete) curve.

t_max_curve

minimum and maximum value of the observed time domain of the (potentially incomplete) curve.

Kt

Number of B-spline basis functions used to estimate mean functions. Default is 8.

periodic

If TRUE, uses periodic b-spline basis functions. Default is FALSE. loss_h_gradient() is currently only available for periodic = FALSE.

warping

If nonparametric (default), inverse warping functions are estimated nonparametrically. If piecewise_linear2 they follow a piecewise linear function with 2 knots. loss_h_gradient() is currently only available for warping = "nonparametric".

Value

A numeric vector of spline coefficients for the gradient of the loss function.

Author(s)

Julia Wrobel [e-mail], Alexander Bauer [e-mail]