Robust GMM parameter estimation via the K-BM algorithm

In this paper, we develop an expectation-maximization (EM)-like scheme, called K-BM, for iterative numerical computation of the minimum K-divergence estimator (MKDE). This estimator utilizes Parzen's non-parameteric Kernel density estimate to down weight low density areas attributed to outliers. Similarly to the standard EM algorithm, the K-BM involves successive Maximizations of lower Bounds on the objective function of the MKDE. Differently from EM, these bounds do not rely on conditional expectations only. The proposed K-BM algorithm is applied to robust parameter estimation of a finite-order multivariate Gaussian mixture model (GMM). Simulation studies illustrate the performance advantage of the K-BM as compared to other state-of-the-art robust GMM estimators.