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Maximum Likelihood Estimation of Gaussian Mixture Models Using Stochastic Search C aglar Aria
 

Summary: Maximum Likelihood Estimation of Gaussian Mixture Models Using Stochastic Search
C aglar Aria
, Selim Aksoyb,
, Orhan Arikana
aDepartment of Electrical and Electronics Engineering, Bilkent University, Ankara, 06800, Turkey
bDepartment of Computer Engineering, Bilkent University, Ankara, 06800, Turkey
Abstract
Gaussian mixture models (GMM), commonly used in pattern recognition and machine learning, provide a flexible probabilistic
model for the data. The conventional expectation-maximization (EM) algorithm for the maximum likelihood estimation of the
parameters of GMMs is very sensitive to initialization and easily gets trapped in local maxima. Stochastic search algorithms have
been popular alternatives for global optimization but their uses for GMM estimation have been limited to constrained models using
identity or diagonal covariance matrices. Our major contributions in this paper are twofold. First, we present a novel parametrization
for arbitrary covariance matrices that allow independent updating of individual parameters while retaining validity of the resultant
matrices. Second, we propose an effective parameter matching technique to mitigate the issues related with the existence of
multiple candidate solutions that are equivalent under permutations of the GMM components. Experiments on synthetic and real
data sets show that the proposed framework has a robust performance and achieves significantly higher likelihood values than the
EM algorithm.
Keywords: Gaussian mixture models, maximum likelihood estimation, expectation-maximization, covariance parametrization,
identifiability, stochastic search, particle swarm optimization
1. Introduction

  

Source: Aksoy, Selim - Department of Computer Engineering, Bilkent University

 

Collections: Computer Technologies and Information Sciences