A two-round variant of EM for Gaussian mixtures, S. Dasgupta and L. J. Schulman. Proceedings of the 16'th UAI (Conference on Uncertainty in Artificial Intelligence), 2000.

We show that, given data from a mixture of $k$ well-separated spherical Gaussians in ${\mathbb R}^n$, a simple two-round variant of EM will, with high probability, learn the centers of the Gaussians to near-optimal precision, if the dimension is high ($n \gg \log k$). We relate this to previous theoretical and empirical work on the EM algorithm.