Model Selection and Estimation of a Finite Shifted-Scaled Dirichlet Mixture Model

This paper proposes an unsupervised learning algorithm for a finite mixture model of shifted-scaled Dirichlet distributions. Maximum likelihood and Newton raphson approaches are used for parameters estimation. In this research work, we address the flexibility challenge of the Dirichlet distribution by having another set of parameters for the location (beside the Scale parameter) that add functional probability models. This paper evaluates the capability of the discussed model to perform the categorization using both synthetic and real data related to the medical science to help in selecting wart treatment method, in the business field to detect the reasons behind employees absenteeism, and the writer identification application to define the author of off-line handwritten documents. We also compare the model performance against scaled Dirichlet, the classic Dirichlet, and Gaussian mixture models. Finally, experimental results are presented on the selected datasets. Besides, we apply the minimum message length to determine the optimal number of the components found within each dataset.