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.

翻译：我们考虑估计高斯混合密度的参数,其中给出的成分数量最能代表一组加权样品。我们通过将样品视为具有加权成分的连续域的离散Dirac混合物密度来对样品进行密度判读。因此,高斯混合装配被视为密度再适应。为了加速计算,建议了一种预期-最大化方法,不仅适当考虑到样品位置,而且考虑到相应的重量。这表明文献中的方法不正确处理重量,从而得出错误的估计数。这用简单的反示例来证明。拟议方法在任何尺寸中都使用与标准高斯混合测算器相同的计算负荷,用于未加权样品。