compute_elastic_mean: Compute a elastic mean for a collection of curves

In elasdics: Elastic Analysis of Sparse, Dense and Irregular Curves

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_mean.

Usage

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.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.
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

Value

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.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 mean.
closed	TRUE if the mean is supposed to be a closed curve.

Examples

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)

elasdics documentation built on June 22, 2024, 12:27 p.m.