Tech Report Available: EM algorithm

[Michael Jordan]

FTP-host: psyche.mit.edu
FTP-file: pub/jordan/AIM-1520.ps.Z

The following paper is now available by anonymous ftp.

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On Convergence Properties of the EM Algorithm for
Gaussian Mixtures (10 pages)

Lei Xu and Michael I. Jordan
CUHK and MIT
 
Abstract:

We build up the mathematical connection between the
``Expectation-Maximization'' (EM) algorithm and gradient-based
approaches for maximum likelihood learning of finite Gaussian
mixtures.  We show that the EM step in parameter space is
obtained from the gradient via a projection matrix $P$, and
we provide an explicit expression for the matrix.  We then
analyze the convergence of EM in terms of special properties
of $P$ and provide new results analyzing the effect that $P$
has on the likelihood surface.  Based on these mathematical
results, we present a comparative discussion of the advantages
and disadvantages of EM and other algorithms for the
learning of Gaussian mixture models.

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