  We present a clustering method and provide a theoretical analysis and an
explanation to a phenomenon encountered in the applied statistical literature
since the 1990's. This phenomenon is the natural adaptability of the order when
using a clustering method derived from the famous EM algorithm. We define a new
statistic, the relative entropic order, that represents the number of clumps in
the target distribution. We prove in particular that the empirical version of
this relative entropic order is consistent. Our approach is easy to implement
and has a high potential of applications. Perspectives of this works are
algorithmic and theoretical, with possible natural extensions to various cases
such as dependent or multidimensional data.
