fit_elastic_regression {elasdics} R Documentation

## 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
)


### 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

### 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.

### 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)


[Package elasdics version 1.1.3 Index]