  It has been noticed that some external CVIs exhibit a preferential bias
towards a larger or smaller number of clusters which is monotonic (directly or
inversely) in the number of clusters in candidate partitions. This type of bias
is caused by the functional form of the CVI model. For example, the popular
Rand index (RI) exhibits a monotone increasing (NCinc) bias, while the Jaccard
Index (JI) index suffers from a monotone decreasing (NCdec) bias. This type of
bias has been previously recognized in the literature. In this work, we
identify a new type of bias arising from the distribution of the ground truth
(reference) partition against which candidate partitions are compared. We call
this new type of bias ground truth (GT) bias. This type of bias occurs if a
change in the reference partition causes a change in the bias status (e.g.,
NCinc, NCdec) of a CVI. For example, NCinc bias in the RI can be changed to
NCdec bias by skewing the distribution of clusters in the ground truth
partition. It is important for users to be aware of this new type of biased
behaviour, since it may affect the interpretations of CVI results. The
objective of this article is to study the empirical and theoretical
implications of GT bias. To the best of our knowledge, this is the first
extensive study of such a property for external cluster validity indices.
