  Expectation-Maximization (EM) algorithm is a widely used iterative algorithm
for computing (local) maximum likelihood estimate (MLE). It can be used in an
extensive range of problems, including the clustering of data based on the
Gaussian mixture model (GMM). Numerical instability and convergence problems
may arise in situations where the sample size is not much larger than the data
dimensionality. In such low sample support (LSS) settings, the covariance
matrix update in the EM-GMM algorithm may become singular or poorly
conditioned, causing the algorithm to crash. On the other hand, in many signal
processing problems, a priori information can be available indicating certain
structures for different cluster covariance matrices. In this paper, we present
a regularized EM algorithm for GMM-s that can make efficient use of such prior
knowledge as well as cope with LSS situations. The method aims to maximize a
penalized GMM likelihood where regularized estimation may be used to ensure
positive definiteness of covariance matrix updates and shrink the estimators
towards some structured target covariance matrices. We show that the
theoretical guarantees of convergence hold, leading to better performing EM
algorithm for structured covariance matrix models or with low sample settings.
