## The Impact of Random Models on Clustering Similarity

*Alexander J. Gates, Yong-Yeol Ahn*; 18(87):1−28, 2017.

### Abstract

Clustering is a central approach for unsupervised learning.
After clustering is applied, the most fundamental analysis is to
quantitatively compare clusterings. Such comparisons are crucial
for the evaluation of clustering methods as well as other tasks
such as consensus clustering. It is often argued that, in order
to establish a baseline, clustering similarity should be
assessed in the context of a random ensemble of clusterings. The
prevailing assumption for the random clustering ensemble is the
permutation model in which the number and sizes of clusters are
fixed. However, this assumption does not necessarily hold in
practice; for example, multiple runs of K-means clustering
reurns clusterings with a fixed number of clusters, while the
cluster size distribution varies greatly. Here, we derive
corrected variants of two clustering similarity measures (the
Rand index and Mutual Information) in the context of two random
clustering ensembles in which the number and sizes of clusters
vary. In addition, we study the impact of one-sided comparisons
in the scenario with a reference clustering. The consequences of
different random models are illustrated using synthetic
examples, handwriting recognition, and gene expression data. We
demonstrate that the choice of random model can have a drastic
impact on the ranking of similar clustering pairs, and the
evaluation of a clustering method with respect to a random
baseline; thus, the choice of random clustering model should be
carefully justified.

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