  We consider estimating the parameters of a Gaussian mixture density with a
given number of components best representing a given set of weighted samples.
We adopt a density interpretation of the samples by viewing them as a discrete
Dirac mixture density over a continuous domain with weighted components. Hence,
Gaussian mixture fitting is viewed as density re-approximation. In order to
speed up computation, an expectation-maximization method is proposed that
properly considers not only the sample locations, but also the corresponding
weights. It is shown that methods from literature do not treat the weights
correctly, resulting in wrong estimates. This is demonstrated with simple
counterexamples. The proposed method works in any number of dimensions with the
same computational load as standard Gaussian mixture estimators for unweighted
samples.
