Robust Clustering with McDonald’s Beta-Liouville Mixture Models for Proportional Data

In this work, we study the problem of determining a proportional data structure in the absence of prior information about the number of clusters. We use finite mixture models to represent the data samples. These models are based on the McDonald’s Beta-Liouville distribution, which is a novel distribution that combines the salient characteristics of the Liouville and McDonald’s Beta distributions. When compared to common distributions like the Dirichlet, it provides higher flexibility and a more robust covariance structure. But, one major problem in mixture modeling is figuring out how many clusters to have. In this instance, the minimum message length (MML) technique is used to determine the number of clusters. In addition, as part of the Expectation Maximization procedure, the complexity of the mixture model - that is, the total number of components - can be automatically and concurrently determined while estimating the parameters. Our suggested approach is utilized in medical settings, specifically to focus medication for individuals with heart disease based on clinical data and analyze breast tissue taking into account histological scans. When it comes to data with strictly bounded values and an asymmetric distribution, the McDonald’s Beta-Liouville mixture model outperforms the Gaussian mixture model (GMM) and the Dirichlet mixture model (DMM). The novel McDonald’s Beta-Liouville mixing model (McDonald’s BLMM) is used to model two real-world datasets. The results demonstrate that this model performs well and is more accurate than the GMM and DMM.