Take the 2-minute tour ×  For a collection of points in
$\mathbb{R}^n$, is there a statistic that I can compute which
will estimate the number of clusters with some level of
confidence?  share|improve this question  5 Answers 5  up vote 4
down vote accepted  This is an age-old question, which actually
does not have (I think even cannot have) a definite answer,
because first you need to define what you mean by a cluster and
so on. A famous saying in this regard is that "cluster is in the
eye of a beholder". It is easy to construct examples where
somebody could see one cluster, but somebody else more than one.
This being said, the MDL (minimum description length) principle
would lead you to devise (IMHO) a clustering cost function in a
most principled way, which by optimizing you could the find the
cluster assignments and number of clusters simultaneously. For
multinomial data you can see following: P.Kontkanen,
P.Myllymäki, W.Buntine, J.Rissanen, H.Tirri, An MDL Framework
for Data Clustering. In Advances in M