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

EM algorithm is widely used in clustering domain because of its easy implementation and small storage space. CEM algorithm, which is considered as a classification version of EM algorithm, is another common used clustering algorithm. With the development of technology, we obtain more and more data. This results in slow computation of EM and CEM algorithms. Binning data seems to be efficient in gaining computation time by reducing the number of observations to the number of bins. Thus, EM and CEM algorithms applied to binned data were proposed: binned-EM and bin-EM-CEM algorithms. Moreover, fourteen parsimonious Gaussian mixture models, generated according to eigenvalue decomposition of the variance matrices of the mixture components, have less parameters than the most general model. By applying the EM and CEM algorithms of parsimonious models, estimation process is simplified and then accelerated. In this paper, to combine the advantages of binned data and parsimonious Gaussian mixture models, we develop bin-EM-CEM algorithms of spherical parsimonious Gaussian mixture models.