Robust GMM Parameter Estimation via the K-BM Algorithm

In this paper, we develop an expectation-maximization (EM)-like scheme, called ${\mathcal{K}}$-BM, for iterative numerical computation of the minimum ${\mathcal{K}}$-divergence estimator (M${\mathcal{K}}$DE). This estimator utilizes Parzen’s non-parameteric ${\mathcal{K}}$ernel density estimate to down weight low density areas attributed to outliers. Similarly to the standard EM algorithm, the ${\mathcal{K}}$-BM involves successive Maximizations of lower Bounds on the objective function of the M${\mathcal{K}}$DE. Differently from EM, these bounds do not rely on conditional expectations only. The proposed ${\mathcal{K}}$-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 ${\mathcal{K}}$-BM as compared to other state-of-the-art robust GMM estimators.