Bayesian Latent Class Models

The latent class model (LCM) is a statistical method that introduces a set of latent categorical variables. The main advantage of LCM is that conditional on latent variables, the manifest variables are mutually independent of each other. In some scenarios, the LCM makes the modeling or computation feasible. In some other scenarios, the latent variables themselves are key. In the past a few decades, LCM has been widely applied to many areas such as Engineering, Medicine, Biology and Marketing. In this paper, several LCMs are developed in Bayesian framework to address new challenges in different applications. The first work is about the MR image segmentation. For MR images, we usually need to simultaneously segment multiple images, which are believed to have similar segmentation results. In our co-segmentation model, a Markov random field prior is utilized to encourage the information sharing. Clustering is usually regarded as an unsupervised problem. In our second work, we extend the clustering into supervised setting. This supervised clustering is evaluated in the application of market segmentation. In our third work, we relax the all-feature-in and all-object-in assumptions of the existing clustering approaches and propose a novel model called Multiple Partition Process (MPP) to obtain multiple clustering structures from the data. This MPP model is applied into the clustering of the breast cancer microarray data. In the last part of this paper, our future work is represented