Fuzzy Clustering using Levenberg-Marquardt Optimization and Deterministic Anneal

In this paper, we address the generic problem of unsupervised data clustering within a fuzzy framework. We show that this problem can be formulated as a least mean square vector cost function and propose an iterative solution procedure which utilizes the Levenberg-Marquardt optimization technique. As such, we develop an algorithm which is capable of performing the stated task through utilizing abstract notions of data item, cluster, and data item-to-cluster distance. We demonstrate that the fuzzifier can be utilized as a temperature factor, in order to set up a Deterministic Annealing framework that provides assurance that the derived loss function converges to an acceptable minimum. This is important because the developed method includes an additional layer of numerical optimization on top of the structure commonly used in the literature. This paper includes the derivation of the cost function as well as the outline of the developed solution procedure. We carry sample problem instances from six problem classes and discuss different aspects of the developed method. Finally, we provide a potential next step for this work.