kplus_objective {anticlust} | R Documentation |

Objective value for the k-plus criterion

kplus_objective(x, clusters)

`x` |
A vector, matrix or data.frame of data points. Rows correspond to elements and columns correspond to features. A vector represents a single feature. |

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

The k-plus criterion is an extension of the k-means criterion
(i.e., the "variance", see `variance_objective`

). The
standard k-means objective is high if the means of the input
variables are similar between clusters, but there is no guarantee
that the standard deviations will also be similar (in fact,
maximizing the k-means objective tends to decrease similarity in
standard deviations in comparison to a completely random
assignment). However, to achieve overall between-group similarity,
it is desirable that the spread of the data is also similar between
groups—and not just the means. This is accomplished by maximizing
the k-plus criterion that also incorporates the standard deviations
of the input variables.

Equalizing means and standard deviations simultaneously is
accomplished by internally appending new variables to the data
input `x`

, one new variable for each column in `x`

. These
new variables contain the squared difference of each data point to
the mean of the respective column, and are then included—in
addition to the original data—in standard k-means
anticlustering. This way, the average squared deviation of the data
points to the means becomes similar between groups, which is the
variance. Hence, the k-plus criterion simultaneously represents
similarity in means and variance (and thus, the standard
deviation), and can be used to simultaneously equalize the mean and
the spread of the data.

The value of the k-plus criterion.

K-plus anticlustering has newly been implemented in the package
anticlust (available since version 0.5.2). The author is currently
working on a paper detailing the objective's background, but has
already made the methodology available as its results have been
very convincing thus far (e.g., check out the examples below). When
using k-plus anticlustering in your research, it would be courteous
to cite Papenberg and Klau (2020) as the primary `anticlust`

reference, even though the criterion has not been described in that
paper. In doubt, contact the author to inquire whether a new
reference is available, or check out the package website
(https://github.com/m-Py/anticlust).

Martin Papenberg martin.papenberg@hhu.de

Papenberg, M., & Klau, G. W. (2020). Using anticlustering to partition data sets into equivalent parts. Psychological Methods, 26(2), 161–174. https://doi.org/10.1037/met0000301.

data(schaper2019) features <- schaper2019[, 3:6] # Optimize k-plus criterion kplus_groups <- anticlustering( features, K = 3, objective = "kplus" ) # Optimize normal k-means criterion kmeans_groups <- anticlustering( features, K = 3, objective = "variance" ) # Compute k-plus criterion (k-plus is much better here) kplus_objective(features, kplus_groups) kplus_objective(features, kmeans_groups) # Compare to k-means criterion (k-plus not much worse here) variance_objective(features, kplus_groups) variance_objective(features, kmeans_groups) # Compare means and standard deviations after k-means and k-plus # anticlustering (the standard deviations are usually much closer # after k-plus anticlustering, but there is only little to no # difference with regard to the means) mean_sd_tab(features, kplus_groups) mean_sd_tab(features, kmeans_groups)

[Package *anticlust* version 0.6.0 Index]