# Compute a elastic mean for a collection of curves Computes a Fréchet mean for the curves stored in `data_curves`) with respect to the elastic distance. Constructor function for class `elastic_mean`. ```r compute_elastic_mean( data_curves, knots = seq(0, 1, len = 5), type = c("smooth", "polygon"), closed = FALSE, eps = 0.01, pen_factor = 100, max_iter = 50 ) ``` ## Arguments - `data_curves`: list of `data.frame`s 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. - `knots`: set of knots for the mean spline curve - `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. - `eps`: the algorithm stops if L2 norm of coefficients changes less - `pen_factor`: penalty factor forcing the mean to be closed - `max_iter`: maximal number of iterations ## Returns an object of class `elastic_mean`, which is a `list` with entries - **type**: "smooth" if mean was modeled using linear srv-splines or "polygon" if constant srv-splines are used - **coefs**: spline coeffiecients - **knots**: spline knots - **data_curves**: list of `data.frame`s 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 mean. - **closed**: `TRUE` if the mean is supposed to be a closed curve. ## Examples ```r curve <- function(t){ rbind(t*cos(13*t), t*sin(13*t)) } set.seed(18) data_curves <- lapply(1:4, function(i){ m <- sample(10:15, 1) delta <- abs(rnorm(m, mean = 1, sd = 0.05)) t <- cumsum(delta)/sum(delta) data.frame(t(curve(t)) + 0.07*t*matrix(cumsum(rnorm(2*length(delta))), ncol = 2)) }) #compute elastic means knots <- seq(0,1, length = 11) smooth_elastic_mean <- compute_elastic_mean(data_curves, knots = knots) plot(smooth_elastic_mean) knots <- seq(0,1, length = 15) polygon_elastic_mean <- compute_elastic_mean(data_curves, knots = knots, type = "poly") lines(get_evals(polygon_elastic_mean), col = "blue", lwd = 2) #compute closed smooth mean, takes a little longer knots <- seq(0,1, length = 11) closed_elastic_mean <- compute_elastic_mean(data_curves, knots = knots, closed = TRUE) plot(closed_elastic_mean) ```

compute_elastic_mean function