Em Algorithm For Dirichlet Samples And Its Application To Movie Data

Dirichlet samples are common in economics and many other fields though it has a relatively complex distribution form. Especially in the era of big data, many datasets can be transformed into compositional data which conforms to Dirichlet distributions. The present work first explores EM algorithm for Dirichlet samples and describes its mathematical iteration procedure. Then, the finite sample performance of the proposed method is evaluated using extensive simulations, and the results indicate that the proposed procedure is successful. Moreover, we apply the method to expert rating data from an official movie website, which is an important social media in China. Results show that EM algorithm has a good performance on categorizing the movies. All the movies are classified into two extremely different clusters, of which one represents movies with high quality and the other represents movies with hybrid styles. Further research will extend the method from independent Dirichlet distributions to dependent distributions which are more common situations in real world.