Bin-EM-CEM algorithms of general parsimonious Gaussian mixture models for binned data clustering

Data binning is a well-known data pre-processing technique in statistics. It was applied to model-based clustering approaches to reduce the number of data and facilitate the processing. EM and CEM algorithms are commonly used in model-based approaches. Thus EM and CEM algorithms applied to binned data were developed: binned-EM algorithm for mixture approach, and bin-EM-CEM algorithm for classification approach. At another side, fourteen parsimonious Gaussian mixture models for EM and CEM algorithms were proposed by considering a parametrization of the variance matrices of the clusters. Due to different characteristics of each model, fourteen models can adapt to data of different structures so as to simplify the clustering process. The experimental results of EM algorithms of fourteen parsimonious models also show that the model which fits the data gives a better result than the other models. Previously, binned-EM algorithms of fourteen parsimonious Gaussian mixture models were developed. The result shows to be of interest to combine the advantages of binned data and parsimonious models on model-based clustering approaches. So in this paper, we develop bin-EM-CEM algorithms of the eight most general parsimonious Gaussian mixture models. The performances of the developed algorithms applied to different models of data are studied and analyzed.