When considering Gaussian mixture models (GMM) one efficient algorithm is the Expectation-Minimization (EM) algorithm. The E-step famously determines the degree of membership.
For example, given a GMM with two Gaussians (normal distributions) $N_1,N_2$ and a dataset $X$ of samples, the E-step will try to determine, provide a probability, if a given sample $x_s$ has been sampled from $N_1$ or from $N_2$.
Can the E-step be substituted with some form of (integer) linear programming?
I have seen references such as this http://imagine.enpc.fr/~komodakn/publications/docs/NIPS09_clustering.pdf but I cannot find a direct and simple way to fomrulate this problem easily in say MATLAB.
Any references would be appreciated.