Another Version of the Block EM Algorithm

While most clustering procedures aim to construct an optimal partition of objects or, sometimes, of variables, there are other methods, called block clustering methods, which consider simultaneously the two sets and organize the data into homogeneous blocks. Recently, we have proposed a new mixture model called a block mixture model that addresses this situation. Our model allows one to embed simultaneous clustering of objects and variables through a mixture approach. We use maximum likelihood (ML) to implement the method, and have developed a new EM algorithm to estimate the parameters of this model. This requires an approximation of the likelihood and we propose an alternating-optimization algorithm, which is compared to another version of EM based on an interpretation given by Neal and Hinton. The comparison is performed through numerical experiments on simulated binary data.