||In simulation studies based on many synthetic and real datasets, we
found out that subsampling has a weaker behavior in ﬁnding of the true number
of clusters K than bootstrapping (Mucha and Bartel 2014, 2015, Mucha 2016).
But why? Based on further investigations, here especially concerning the Kmeans
clustering with the comparison of bootstrapping and a special version of
subsampling named “Boot2Sub”, we try to answer this question. In subsampling,
usually a parameter H, the cardinality of the drawn subsample, has to be prespeciﬁed.
Its speciﬁcation means an additional serious problem. The way out
would be to take the bootstrap sample but discard multiple points. We call such a
special subsampling scheme “Boot2Sub”. Then, bootstrapping and subsampling
“Boot2Sub” result exactly in the same subset of drawn observations. This way
allows us to make fair direct comparisons of the performance of bootstrapping
and subsampling. As a result of the assessment of applications to generated and
real datasets, the conjecture arises that multiple points play an important role
for the validation of the true number of clusters in K-means clustering.