Compute the diversity for a given clustering.
diversity_objective(x, clusters)The data input. Can be one of two structures: (1) A data matrix
where rows correspond to elements and columns correspond to
features (a single numeric feature can be passed as a vector). (2)
An N x N matrix dissimilarity matrix; can be an object of class
dist (e.g., returned by dist or
as.dist) or a matrix where the entries of
the upper and lower triangular matrix represent the pairwise
dissimilarities.
A vector representing (anti)clusters (e.g.,
returned by anticlustering).
The cluster editing objective
The objective function used in (anti)cluster editing is the
diversity, i.e., the sum of the pairwise distances between elements
within the same groups. When the input x is a feature
matrix, the Euclidean distance is computed as the basic distance
unit of this objective.
Brusco, M. J., Cradit, J. D., & Steinley, D. (2020). Combining diversity and dispersion criteria for anticlustering: A bicriterion approach. British Journal of Mathematical and Statistical Psychology, 73, 275-396. https://doi.org/10.1111/bmsp.12186
Papenberg, M., & Klau, G. W. (2021). Using anticlustering to partition data sets into equivalent parts. Psychological Methods, 26(2), 161–174. https://doi.org/10.1037/met0000301.
data(iris)
distances <- dist(iris[1:60, -5])
## Clustering
clusters <- balanced_clustering(distances, K = 3)
# This is low:
diversity_objective(distances, clusters)
#> [1] 599.9749
## Anticlustering
anticlusters <- anticlustering(distances, K = 3)
# This is higher:
diversity_objective(distances, anticlusters)
#> [1] 874.6245