應用逐步EM演算法於混合廻歸模型估計之研究

Mixture regressions, also known as switching regressions or clusterwise regressions, are used to determine the relationship between variables from several unknown latent groups. It has been widely applied in many areas such as econometrics, biology, epidemiology, and engineering and has been a longstanding topic in the research of model-based clustering. The mixture likelihood approach associated with the Expectation and Maximization (EM) algorithm is a popular and most often used for estimating mixture regression models. However, EM the performance of EM heavily depends on the initial values. For example, the convergence speed of EM and its ability to locate the global maximum can be seriously affected. Although EM c-regression algorithm (EMCR) has the trouble with initial values but few researches considered this problem. Besides, EM requires the number of regression models given as a priori, however, it is rarely known in real applications. In this research, we propose a schema of nested stepwise procedure for EMCR, called a stepwise EMCR (SEMCR) method, which repeats EMCR on a series of nested subsets using the clustering results of the previous subset as good initial values for EMCR on the succeeding subset. After selecting the smallest subset D1 at the location where c regression models separate adequately, the number of clusters and the cluster centers in D1 can be extracted by the modified mountain method, and hence data in D1 can be partitioned properly which provides good initials for the following EMCR. The proposed SEMCR is unsupervised without initialization and robust to leverage outliers. Several experiments and real examples demonstrate the superiority and effectiveness of the proposed SEMCR method.