Creates a GaussianMixture from the selected TableOfReal by an expectation-maximization procedure.
The Expectation–Maximization (EM) algorithm is an iterative procedure to maximize the likelihood of the data given a model. For a GaussianMixture, the parameters in the model are the centers and the covariances of all components in the mixture and their mixing probabilities.
The number of parameters depends on the number of components in the mixture and the dimension of the data. For a full covariance matrix we have to find dimension(dimension+1)/2 matrix elements and another dimension vector elements for its center. This makes the total number of parameters that have to be estimated for a mixture with Number of components components equal to numberOfComponents · dimension(dimension+3)/2 + numberOfComponents.
For diagonal covariance matrices the number of parameters reduces considerably.
The EM iteration has to start with a sensible initial guess for all the parameters. For the initial guess, we derive our centers from positions on the 1-σ ellipse in the plane spanned by the first two principal components. We then make all covariance matrices equal to a scaled down version of the total covariance matrix where the scaling factor depends on the number of components and the quotient of the between and within variance. Initialy all mixing probabilities will be chosen equal.
How to proceed from the initial guess with the EM to find the optimal values for all the parameters in the Gaussian mixture is explained in great detail by Bishop (2006).
© djmw, September 30, 2015