Entropy-Randomized Clustering

Abstract

This paper proposes a clustering method based on a randomized representation of an ensemble of possible clusters with a probability distribution. The concept of a cluster indicator is introduced as the average distance between the objects included in the cluster. The indicators averaged over the entire ensemble are considered the latter’s characteristics. The optimal distribution of clusters is determined using the randomized machine learning approach: an entropy functional is maximized with respect to the probability distribution subject to constraints imposed on the averaged indicator of the cluster ensemble. The resulting entropy-optimal cluster corresponds to the maximum of the optimal probability distribution. This method is developed for binary clustering as a basic procedure. Its extension to t-ary clustering is considered. Some illustrative examples of entropy-randomized clustering are given.

Keywords

• randomized clustering
• Boltzmann and Fermi entropies
• indicator matrix
• binary clustering
• t-ary clustering
• finite-dimensional and functional problems