Comparison of the mixture and the classification maximum likelihood in cluster analysis with binary data

In this paper we propose to extend the comparison between the maximum likelihood and the classification maximum likelihood approaches for the Gaussian mixture (Ganesalingam, 1989; Celeux and Govaert, 1993) in the case of binary data, To this end, we use Bernoulli distribution mixtures. As with continuous data, two situations are discussed: first where mixing proportions are taken to be equal and secondly where they are unknown. The comparison realized with Monte-Carlo numerical experiments confirms the results obtained with continuous data. The choice of the approach depends on the size of the sample but assumptions about the mixing proportions are more important than the choice between the two approaches.