From Mixtures to Mixing

Mixture models such as Gaussian mixture models and mixing models such as Independent components analysis are used in situations where a number of hidden components are responsible for generating observed data. There is a fundamental difference between these two types of models. In mixture models, it is assumed that a data point comes from one of the components, and which component is unknown. In mixing models, a data point comes from a mixing of all the components, and the mixing proportion is unknown. But there are cases where data follows neither of these processes. For example, in image segmentation problems pixels can be attributed to a single object or they could be mix of two or more objects. In this project we develop a model to combine mixture and mixing models. We use the Dirichlet distribution to control the amount of mixture and mixing. We show some of the difficulties associated with this approach and propose some solutions. We validate the model on MRI data. The results are compared with Gaussian mixture models.