Finite mixture models are powerful and progressively important probabilistic tools in machine learning. The practicality of these inference engines is widely acknowledged by employing them in various areas of science and technology which involve the statistical modeling of multimodal and complex data. One of the crucial tasks that should be addressed in mixture models and unsupervised learning problem is defining the number of clusters which best describe the data. This article proposes a clustering framework for learning a finite mixture model based on a bivariate Beta distribution with three parameters and the proper number of clusters is determined by Minimum Message Length (MML). The feasibility and effectiveness of our work are demonstrated by real world challenging applications such as image segmentation and occupancy estimation in smart buildings.