  The Expectation-Maximization (EM) algorithm is one of the most popular
methods used to solve the problem of parametric distribution-based clustering
in unsupervised learning. In this paper, we propose to analyze a generalized EM
(GEM) algorithm in the context of Gaussian mixture models, where the
maximization step in the EM is replaced by an increasing step. We show that
this GEM algorithm can be understood as a linear time-invariant (LTI) system
with a feedback nonlinearity. Therefore, we explore some of its convergence
properties by leveraging tools from robust control theory. Lastly, we explain
how the proposed GEM can be designed, and present a pedagogical example to
understand the advantages of the proposed approach.
