Adaptative clustering by minimization of the mixing entropy criterion

TL;DR

This paper introduces an adaptive clustering method based on minimizing a new mixing entropy criterion, providing theoretical guarantees and explaining the natural adaptability of clustering order in EM-based methods.

Contribution

It proposes a novel clustering approach with a new statistic, the relative entropic order, and proves its consistency, enhancing understanding and application of adaptive clustering techniques.

Findings

The empirical relative entropic order is consistent.

The method is easy to implement and adaptable.

Potential extensions to complex data types.

Abstract

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.