Convergence Analysis of Gradient EM for Multi-component Gaussian Mixture
arXiv:1705.08530
Abstract
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.
36 pages
References in corpus (7)
- A Two-round Variant of EM for Gaussian Mixtures
- Statistical and Computational Guarantees of Lloyd's Algorithm and its Variants
- Global analysis of Expectation Maximization for mixtures of two Gaussians
- Local Maxima in the Likelihood of Gaussian Mixture Models: Structural Results and Algorithmic Consequences
- Concentration in unbounded metric spaces and algorithmic stability
- Clustering with Spectral Norm and the k-means Algorithm
- On Robustness of Kernel Clustering