Finding cluster centers and sizes via multinomial parameterization

The clustering problem consists in dividing a data set into groups of observations that are similar within but different across. This paper presents a method for assessment the clusters centers and sizes in a non-linear least squares optimization with multinomial parameterization. The method is especially useful for large data sets as it operates on the summary statistics only. This approach also works for the problem of finding clusters' centers and sizes by the covariance matrix when the original data is not available. Estimation of the clusters centers and sizes can be followed by actual clustering. Example of application to marketing research problem is discussed.