A Novel Bayesian probabilistic distance clustering algorithm

Recently, Tortora et al. (SN Comput Sci 1:65, 2020) introduced two probabilistic d-clustering algorithms based on the multivariate Gaussian distribution and multivariate Student-t distributions, which exhibit superior performance compared to probabilistic d-clustering and k-means algorithms. However, these proposed algorithms may need help when the variances of individual clusters are heterogeneous. This paper presents a unified Bayesian approach to Gaussian probabilistic distance clustering to address this issue, employing the Gibbs posterior. We derived a closed-form posterior distribution for each unknown parameter using this approach. The effectiveness of the extended method was demonstrated through two numerical examples, including one simulation study and one real data analysis based on three datasets. The proposed method was further compared with conventional methods, demonstrating its superior accuracy. Simulation studies and real data analyses indicate that in many cases, mainly when there is correlation, overlap, or a data variance greater than one, as well as when overlap alone exists, the Bayesian Gaussian probabilistic distance clustering algorithm outperforms the Gaussian probabilistic distance clustering algorithm.