In this paper, we propose a new method for automated flow cytometry data analysis. By modeling a multidimensional probability distribution as a mixture of simpler distributions, we can reformulate the problem as a coupled tensor approximation of 3D marginals. In order to reduce the computational load, we use partially coupled strategies. We also propose a grouping of rank-one components together with a new visualization of the results. We demonstrate the usefulness of the proposed methodology on simulated and real data.