diversity_objective {anticlust}

(Anti)cluster editing "diversity" objective

Description

Compute the diversity for a given clustering.

Usage

diversity_objective(x, clusters)

Arguments

x

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.

clusters

A vector representing (anti)clusters (e.g., returned by anticlustering).

Details

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.

Value

The cluster editing objective

Author(s)

Martin Papenberg [e-mail]

References

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.

Examples

data(iris)
distances <- dist(iris[1:60, -5])
## Clustering
clusters <- balanced_clustering(distances, K = 3)
# This is low:
diversity_objective(distances, clusters)
## Anticlustering
anticlusters <- anticlustering(distances, K = 3)
# This is higher:
diversity_objective(distances, anticlusters)