Fuzzy Clustering for Responsive Data

The unsupervised clustering of a weighted group of data items, into sets which comply with a notion of homogeneity specific to a particular problem class, is a classical pattern classification problem. Among the different approaches to this problem, fuzzy and possibilistic clustering, and their different variations and combinations, have been studied in the last decades. That study, however, has often been focused on a particular data item or cluster model and has been generally geared towards identifying a particular model of homogeneity. Also, many available models are in essence engineered based on the intuition of the researchers and convoluted and complicated control parameters, regularization terms, and concepts are often incorporated into the mathematical models in order to yield acceptable results. In this paper, we advocate for a derivation-based approach, which utilizes Bayesian inference in order to assess the loss in a generic clustering problem, independent of the particularities of data and cluster models and the notion of homogeneity applicable to any particular problem class. Subsequently, we utilize the organic framework developed in this work in order to address data items which actively respond to the clustering effort. This is distinctly different from the available literature, in which data items are passively subjected to the clustering process. The utilization of an inference-based loss model, which avoids exogenous provisions based on intuition and researcher heuristics, as well as independence from a particular problem class and the introduction of the concept of data responsiveness, to our understanding, are novel to this paper.