Finite Mixture Models For Cluster Based On Exponential Family Of Distributions

Finite mixture models for clustering are very important clustered models which combine two methods as parametric and non-parametric. Exponential family of distributions are also very significant and frequency in Probability of distributions. By means of clustering we can extract some very significant messages which accord with a certain regular rules, our work and study can be bettered and our practical methods also can be improved by these messages.We have deduced some common expressions in relation to finite mixture models of exponential family of distributions with Bayesian posterior probability. In this article, EM algorithm was applied to estimate the parameters and expressions of the models; Newton iteration method and Monte Carlo stochastic simulation are used to compute the parameters, BIC criterion was utilized to confirm the concrete number of the models. And then in the process of simulations and compensations, Several Gamma distributions with diverse parameters and datum were used as an example to fit the models we have deduced previously, besides, Bayesian posterior probability is applied to classify datum, and the branch number of models was computed by it. The final result indicates that the proposed algorithm and expressions can effectively estimate and learn the parameters and models of gamma distributions. Furthermore, In order to improve the accuracy of this model, ensemble learning method in machine learning was proposed or introduced. Using it we obtained the models of finite mixture models of exponential family of distributions.