Using anticlustering to partition data sets into equivalent parts.

Abstract

Numerous applications in psychological research require that a pool of elements is partitioned into multiple parts. While many applications seek groups that are well-separated, i.e., dissimilar from each other, others require the different groups to be as similar as possible. Examples include the assignment of students to parallel courses, assembling stimulus sets in experimental psychology, splitting achievement tests into parts of equal difficulty, and dividing a data set for cross validation. We present anticlust, an easy-to-use and free software package for solving these problems fast and in an automated manner. The package anticlust is an open source extension to the R programming language and implements the methodology of anticlustering. Anticlustering divides elements into similar parts, ensuring similarity between groups by enforcing heterogeneity within groups. Thus, anticlustering is the direct reversal of cluster analysis that aims to maximize homogeneity within groups and dissimilarity between groups. Our package anticlust implements two anticlustering criteria, reversing the clustering methods k-means and cluster editing, respectively. In a simulation study, we show that anticlustering returns excellent results and outperforms alternative approaches like random assignment and matching. In three example applications, we illustrate how to apply anticlust on real data sets. We demonstrate how to assign experimental stimuli to equivalent sets based on norming data, how to divide a large data set for cross validation, and how to split a test into parts of equal item difficulty and discrimination.

k-plus Anticlustering: An Improved k-means Criterion for Maximizing Between-Group Similarity

“…Anticlustering thereby reverses the logic of its better known twin-cluster analysis-which seeks homogeneity within clusters and separation between clusters (Rokach & Maimon, 2005). Anticlustering has many applications in research psychology (Brusco et al, 2020;Papenberg & Klau, 2021;Steinley, 2006). Examples include splitting tests into parts of equal difficulty (Gierl et al, 2017), assigning students to work groups (Baker & Powell, 2002), and assigning stimuli to different, but parallel experimental conditions (Lahl & Pietrowsky, 2006).…”

“…Solving anticlustering problems "by hand" is a tedious and time-consuming task, and the quality of manual partitioning is usually subpar. Fortunately, anticlustering problems can be formalized as mathematical optimization problems (e.g., Baker & Powell, 2002;Brusco et al, 2020;Fernández et al, 2013;Späth, 1986) and accessible open source software solutions to tackling these problems exist (Papenberg & Klau, 2021).…”

“…However, other distribution characteristics-such as the variance-are not targeted. Papenberg and Klau (2021) showed that k-means anticlustering tends to over-optimize between-group similarity with regard to the mean at the cost of similarity in variance.…”

Metacognitive differentiation of item memory and source memory in schema-based source monitoring.

“…We split the item pool into three lists each containing 12 bathroom, 12 bedroom, and 12 kitchen items. To obtain three lists that were matched on consistency and inconsistency ratings from Norming Study 2, number of syllables, and word frequency we used the R package anticlust (Papenberg & Klau, 2021).…”

experDesign: stratifying samples into batches with minimal bias

“…• anticlust, at CRAN, divides the samples into similar groups, ensuring similarity by enforcing heterogeneity within groups (Papenberg and Klau 2020). Conceptually it is similar to the clustering method k-means.…”