Generates results of multiple clustering strategies

This function searches for clusters in the input data set using different strategies and generates an object of class mcaps which stores multiple objects of class caps. This is a helper function to facilitate comparison of clustering methods and choice of an optimal one.

Usage

compare_caps(
  x,
  y,
  n_clusters = 1:5,
  is_domain_interval = FALSE,
  transformation = c("identity", "srsf"),
  metric = c("l2", "normalized_l2", "pearson"),
  clustering_method = c("kmeans", "hclust-complete", "hclust-average", "hclust-single",
    "dbscan"),
  warping_class = c("none", "shift", "dilation", "affine", "bpd"),
  centroid_type = c("mean", "medoid", "median", "lowess", "poly"),
  cluster_on_phase = FALSE
)

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.
n_clusters: An integer vector specifying a set of clustering partitions to create. Defaults to 1:5.
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 slope function transformation = "srsf". Defaults to "identity".
metric: A string specifying the metric used to compare curves. Choices are "l2", "normalized_l2" or "pearson". If transformation == "srsf", the metric must be "l2" because the SRSF 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".
clustering_method: A character vector specifying one or more clustering methods to be fit. Choices are "kmeans", "hclust-complete", "hclust-average", "hclust-single" or "dbscan". Defaults to all of them.
warping_class: A character vector specifying one or more classes of warping functions to use for curve alignment. Choices are "affine", "dilation", "none", "shift" or "srsf". Defaults to all of them.
centroid_type: A character vector specifying one or more ways to compute centroids. Choices are "mean", "medoid", "median", "lowess" or "poly". Defaults to all of them.
cluster_on_phase: A boolean specifying whether clustering should be based on phase variation or amplitude variation. Defaults to FALSE which implies amplitude variation.

Value

An object of class mcaps which is a tibble::tibble storing the objects of class caps in correspondence of each combination of possible choices from the input arguments.

Examples

#----------------------------------
# Compare k-means results with k = 1, 2, 3, 4, 5 using mean centroid and
# various warping classes.
if (FALSE) {
sim30_mcaps <- compare_caps(
  x = simulated30_sub$x,
  y = simulated30_sub$y,
  warping_class = c("none", "shift", "dilation", "affine"),
  clustering_method = "kmeans",
  centroid_type = "mean"
)
}

#----------------------------------
# Then visualize the results
# Either with ggplot2 via ggplot2::autoplot(sim30_mcaps)
# or using graphics::plot()
# You can visualize the WSS values:
plot(sim30_mcaps, validation_criterion = "wss", what = "mean")

plot(sim30_mcaps, validation_criterion = "wss", what = "distribution")

# Or the average silhouette values:
plot(sim30_mcaps, validation_criterion = "silhouette", what = "mean")

plot(sim30_mcaps, validation_criterion = "silhouette", what = "distribution")