Browsing by Subject "Stochastic search"
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Item Open Access Maximum likelihood estimation of Gaussian mixture models using stochastic search(Elsevier BV, 2012) Ar, C.; Aksoy, S.; Arıkan, OrhanGaussian mixture models (GMM), commonly used in pattern recognition and machine learning, provide a flexible probabilistic model for the data. The conventional expectationmaximization (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. © 2012 Elsevier Ltd. All rights reserved.Item Open Access Unsupervised classification of remotely sensed images using Gaussian mixture models and particle swarm optimization(IEEE, 2010) Arı, Çağlar; Aksoy, SelimGaussian mixture models (GMM) are widely used for un-supervised classification applications in remote sensing. Expectation-Maximization (EM) is the standard algorithm employed to estimate the parameters of these models. However, such iterative optimization methods can easily get trapped into local maxima. Researchers use population-based stochastic search algorithms to obtain better estimates. We present a novel particle swarm optimization-based algorithm for maximum likelihood estimation of Gaussian mixture models. The proposed approach provides solutions for important problems in effective application of population-based algorithms to the clustering problem. We present a new parametrization for arbitrary covariance matrices that allows independent updating of individual parameters during the search process. We also describe an optimization formulation for identifying the correspondence relations between different parameter orderings of candidate solutions. Experiments on a hyperspectral image show better clustering results compared to the commonly used EM algorithm for estimating GMMs. © 2010 IEEE.