Bayesian Clustering of Fuzzy Feature Vectors Using a Quasi-Likelihood Approach

Bayesian model-based classifiers, both unsupervised and supervised, have been studied extensively, and their value and versatility have been demonstrated on a wide spectrum of applications within science and engineering. A majority of the classifiers are built on the assumption of intrinsic discreteness of the considered data features or on their discretization prior to the modeling. On the other hand, Gaussian mixture classifiers have also been utilized to a large extent for continuous features in the Bayesian framework. Often, the primary reason for discretization in the classification context is the simplification of the analytical and numerical properties of the Bayesian models. However, the discretization can be problematic due to its ad hoc nature and the decreased statistical power to detect the correct classes (or clusters) in the resulting procedure. Here, we introduce an unsupervised classification approach for fuzzy feature vectors that utilizes a discrete model structure while preserving the continuous characteristics of data. This goal is achieved by replacing the ordinary likelihood by a binomial quasi-likelihood to yield an analytical expression for the posterior probability of a given clustering solution. The resulting model can also be justified from an information-theoretic perspective. Our method is shown to yield highly accurate clusterings for challenging synthetic and empirical data sets and to perform favorably compared to some alternative approaches.