  The problem of finding groups in data (cluster analysis) has been extensively
studied by researchers from the fields of Statistics and Computer Science,
among others. However, despite its popularity it is widely recognized that the
investigation of some theoretical aspects of clustering has been relatively
sparse. One of the main reasons for this lack of theoretical results is surely
the fact that, unlike the situation with other statistical problems as
regression or classification, for some of the cluster methodologies it is quite
difficult to specify a population goal to which the data-based clustering
algorithms should try to get close. This paper aims to provide some insight
into the theoretical foundations of the usual nonparametric approach to
clustering, which understands clusters as regions of high density, by
presenting an explicit formulation for the ideal population clustering.
