Linear mixing random measures based mixture models

When observations are organized into groups where commonalties exist amongst them, the traditional clustering models cannot discover shared clusters among groups. In this scenario, the dependent normalized random measures based clustering is a perfect choice. The most interesting property of the proposed LMRM based clustering is that the clusters are assumed to be shared across groups. Hence the problem can be solved immediately. We derive appropriate exchangeable probability partition function, and subsequently also deduce its inference algorithm given any mixture model likelihood. We provide all necessary derivation and solution to this framework. For demonstration, we used mixture of Gaussians likelihood in combination with a dependent structure constructed by linear combinations of completely random measures. Our experiments show superiority performance when using this framework, where the inferred values including both the mixing weights and the number of clusters both respond appropriately to the number of completely random measure used.