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We present a clustering method and provide a theoretical analysis and anexplanation to a phenomenon encountered in the applied statistical literaturesince the 1990's. This phenomenon is the natural adaptability of the order whenusing a clustering method derived from the famous EM algorithm. We define a newstatistic, the relative entropic order, that represents the number of clumps inthe target distribution. We prove in particular that the empirical version ofthis relative entropic order is consistent. Our approach is easy to implementand has a high potential of applications. Perspectives of this works arealgorithmic and theoretical, with possible natural extensions to various casessuch as dependent or multidimensional data.

Adaptative clustering by minimization of the mixing entropy criterion