  In this paper, we study convergence properties of the gradient
Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian
Mixture Models for general number of clusters and mixing coefficients. We
derive the convergence rate depending on the mixing coefficients, minimum and
maximum pairwise distances between the true centers and dimensionality and
number of components; and obtain a near-optimal local contraction radius. While
there have been some recent notable works that derive local convergence rates
for EM in the two equal mixture symmetric GMM, in the more general case, the
derivations need structurally different and non-trivial arguments. We use
recent tools from learning theory and empirical processes to achieve our
theoretical results.
