The fitting of binned data clustering to imprecise data

This paper addresses the problem of taking into account the data imprecision in the clustering of binned data using mixture models and binned EM algorithm. Within the framework of a defects detection problem by acoustic emission control, we were brought to treat a set of points using the EM algorithm applied to a diagonal Gaussian mixture model. This one provides a satisfactory solution but the real time constraints imposed in our problem make its application impossible when the number of points becomes too big. As data sets become larger, data processing becomes increasingly complex and as a result, the data analysis is expensive in computation time. The solution that we propose is to group data and available data thus takes the form of a histogram. Such data are also called binned data. We fit the binning data procedure to imprecise data. We model imprecise data by multivariate uncertainty zones and we propose to assign each uncertainty zone to several bins with percentages proportional to its overlapping surfaces with the bins. The experimental results compare this binning procedure with the classical one (applied to imprecise points) and with the interval EM algorithm considered here as a reference, using simulated data.