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#' Monothetic Clustering Tree Object
#'
#' The structure and objects contained in MonoClust, an object returned from
#' the [MonoClust()] function and used as the input in other functions in the
#' package.
#'
#' @name MonoClust.object
#'
#' @return
#' \describe{
#' \item{frame}{Data frame in the form of a [tibble::tibble()] representing
#' a tree structure with one row for each node. The columns include:
#' \describe{
#' \item{number}{Index of the node. Depth of a node can be derived by
#' `number %/% 2`.}
#' \item{var}{Name of the variable used in the split at a node or
#' `"<leaf>"` if it is a leaf node.}
#' \item{cut}{Splitting value, so values of `var` that are smaller than
#' that go to left branch while values greater than that go to the right
#' branch.}
#' \item{n}{Cluster size, the number of observations in that cluster.}
#' \item{inertia}{Inertia value of the cluster at that node.}
#' \item{bipartsplitrow}{Position of the next split row in the data set
#' (that position will belong to left node (smaller)).}
#' \item{bipartsplitcol}{Position of the next split variable in the data
#' set.}
#' \item{inertiadel}{Proportion of inertia value of the cluster at that
#' node to the inertia of the root.}
#' \item{medoid}{Position of the data point regarded as the medoid of
#' its cluster.}
#' \item{loc}{y-coordinate of the splitting node to facilitate showing
#' on the tree. See [plot.MonoClust()] for details.}
#' \item{split.order}{Order of the splits with root is 0.}
#' \item{inertia_explained}{Percent inertia explained as described in
#' Chavent (2007). It is `1 - (sum(current inertia)/inertial[1])`.}
#' \item{alt}{A nested tibble of alternate splits at a node. It contains
#' `bipartsplitrow` and `bipartsplitcol` with the same meaning above.
#' Note that this is only for information purpose. Currently `monoClust`
#' does not support choosing an alternate splitting route. Running
#' [MonoClust()] with `nclusters = 2` step-by-step can be run if
#' needed.}
#' }}
#' \item{membership}{Vector of the same length as the number of rows in the
#' data, containing the value of `frame$number` corresponding to the leaf
#' node that an observation falls into.}
#' \item{dist}{Distance matrix calculated using the method indicated in
#' `distmethod` argument of [MonoClust()].}
#' \item{terms}{Vector of variable names in the data that were used to split.}
#' \item{centroids}{Data frame with one row for centroid value of each
#' cluster.}
#' \item{medoids}{Named vector of positions of the data points regarded as
#' medoids of clusters.}
#' \item{alt}{Indicator of having an alternate splitting route occurred when
#' splitting.}
#' \item{circularroot}{List of values designed for circular variable in the
#' data set. `var` is the name of circular variable and `cut` is its first
#' best split value. If circular variable is not available, both objects are
#' NULL.}
#' }
#' @references
#' * Chavent, M., Lechevallier, Y., & Briant, O. (2007). DIVCLUS-T: A monothetic
#' divisive hierarchical clustering method. Computational Statistics & Data
#' Analysis, 52(2), 687-701. \doi{10.1016/j.csda.2007.03.013}.
#' @seealso [MonoClust()].
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