“Anti-Bayesian” flat and hierarchical clustering using symmetric quantiloids

Abstract

A Pattern Recognition (PR) system that does not involve labelled samples requires the clustering of the samples into their respective classes before the training and testing can be achieved. All of the reported clustering algorithms (except the one reported in Hammer et al., 2015) operate on Bayesian principles, which is understandable because these principles constitute the basis of optimal PR. Recently, Oommen and his co-authors have proposed a novel, counter-intuitive and pioneering PR scheme that is radically opposed to the Bayesian principle. The rational for this paradigm, referred to as the “Anti-Bayesian” (AB) paradigm, involves classification based on the non-central quantiles of the distributions. This paper, extends the results of Hammer et al. (2015) in many directions. Firstly, we generalize our previous AB clustering Hammer et al. (2015) to handle arbitrary d-dimensional spaces using so-called “quantiloids”. Secondly, we extend the AB paradigm to consider how the clustering can be achieved in hierarchical ways, where we analyze both the Top-Down and the Bottom-Up clustering options. Extensive experimentation, on artificial and on challenging real-life data, demonstrates that our clustering achieves results competitive to the state-of-the-art flat, Top-Down and Bottom-Up clustering approaches, demonstrating the power of the AB paradigm.