elasdics (version 1.1.3)

fit_elastic_regression: Compute a elastic mean for a collection of curves

Description

Computes a Fréchet mean for the curves stored in data_curves with respect to the elastic distance. Constructor function for class elastic_reg_model.

Usage

fit_elastic_regression(
  formula,
  data_curves,
  x_data,
  knots = seq(0, 1, 0.2),
  type = "smooth",
  closed = FALSE,
  max_iter = 10,
  eps = 0.001,
  pre_align = FALSE
)

Value

an object of class elastic_reg_model, which is a list

with entries

type

"smooth" if linear srv-splines or "polygon" if constant srv-splines were used

coefs

spline coeffiecients

knots

spline knots

data_curves

list of data.frames with observed points in each row. First variable t gives the initial parametrization, second variable t_optim the optimal parametrization when the curve is aligned to the model prediction.

closed

TRUE if the regression model fitted closed curves.

Arguments

formula

an object of class "formula" of the form data_curves ~ ...".

data_curves

list of data.frames with observed points in each row. Each variable is one coordinate direction. If there is a variable t, it is treated as the time parametrization, not as an additional coordinate.

x_data

a data.frame with covariates.

knots

set of knots for the parameter curves of the regression model

type

if "smooth" linear srv-splines are used which results in a differentiable mean curve if "polygon" the mean will be piecewise linear.

closed

TRUE if the curves should be treated as closed.

max_iter

maximal number of iterations

eps

the algorithm stops if L2 norm of coefficients changes less

pre_align

TRUE if curves should be pre aligned to the mean

Examples

curve <- function(x_1, x_2, t){
  rbind(2*t*cos(6*t) - x_1*t , x_2*t*sin(6*t))
}
set.seed(18)
x_data <- data.frame(x_1 = runif(10,-1,1), x_2 = runif(10,-1,1))
data_curves <- apply(x_data, 1, function(x){
  m <- sample(10:15, 1)
  delta <- abs(rnorm(m, mean = 1, sd = 0.05))
  t <- cumsum(delta)/sum(delta)
  data.frame(t(curve((x[1] + 1), (x[2] + 2), t))
   + 0.07*t*matrix(cumsum(rnorm(2*length(delta))), ncol = 2))
})
reg_model <- fit_elastic_regression(data_curves ~ x_1 + x_2,
                                    data_curves = data_curves, x_data = x_data)
plot(reg_model)