Computes the distance matrix for functional data with amplitude and phase separation

This function computes the matrix of pairwise distances between curves a functional data sample. This can be achieved with or without phase and amplitude separation, which can be done using a variety of warping classes.

Usage

fdadist(
  x,
  y = NULL,
  is_domain_interval = FALSE,
  transformation = c("identity", "srvf"),
  warping_class = c("none", "shift", "dilation", "affine", "bpd"),
  metric = c("l2", "normalized_l2", "pearson"),
  cluster_on_phase = FALSE,
  labels = NULL
)

Arguments

x: A numeric vector of length \(M\) or a numeric matrix of shape \(N \times M\) or an object of class funData::funData. If a numeric vector or matrix, it specifies the grid(s) of size \(M\) on which each of the \(N\) curves have been observed. If an object of class funData::funData, it contains the whole functional data set and the y argument is not used.
y: Either a numeric matrix of shape \(N \times M\) or a numeric array of shape \(N \times L \times M\) or an object of class fda::fd. If a numeric matrix or array, it specifies the \(N\)-sample of \(L\)-dimensional curves observed on grids of size \(M\). If an object of class fda::fd, it contains all the necessary information about the functional data set to be able to evaluate it on user-defined grids.
is_domain_interval: A boolean specifying whether the sample of curves is defined on a fixed interval. Defaults to FALSE.
transformation: A string specifying the transformation to apply to the original sample of curves. Choices are no transformation (transformation = "identity") or square-root velocity function transformation = "srvf". Defaults to "identity".
warping_class: A string specifying the class of warping functions. Choices are no warping (warping_class = "none"), shift y = x + b (warping_class = "shift"), dilation y = ax (warping_class = "dilation"), affine y = ax + b (warping_class = "affine") or boundary-preserving diffeomorphism (warping_class = "bpd"). Defaults to "none".
metric: A string specifying the metric used to compare curves. Choices are "l2", "normalized_l2" or "pearson". If transformation == "srvf", the metric must be "l2" because the SRVF transform maps absolutely continuous functions to square-integrable functions. If transformation == "identity" and warping_class is either dilation or affine, the metric cab be either "normalized_l2" or "pearson". The L2 distance is indeed not dilation-invariant or affine-invariant. The metric can also be "l2" if warping_class == "shift". Defaults to "l2".
cluster_on_phase: A boolean specifying whether clustering should be based on phase variation or amplitude variation. Defaults to FALSE which implies amplitude variation.
labels: A character vector specifying curve labels. Defaults to NULL which uses sequential numbers as labels.

Value

A stats::dist object storing the distance matrix between the input curves using the metric specified through the argument metric and the warping class specified by the argument warping_class.

Examples

idx <- c(1:5, 11:15, 21:25)
D <- fdadist(simulated30_sub$x[idx, ], simulated30_sub$y[idx, , ])