EM algorithms for Gaussian mixtures with split-and-merge operation

Zhang, Zhihua; Chen, Chibiao; Sun, Jian; Chan, Kap Luk

doi:10.1016/s0031-3203(03)00059-1

Cited by 139 publications

(123 citation statements)

References 14 publications

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“…However, global optimizers have high computational demands and this approach is limited to moderately sized datasets. Other algorithms proposed to deal with the problem of local maxima include versions of EM with split and merge operations [34,36], a greedy learning method [35], and a component-wise method [10]. Some of these approaches try to estimate simultaneously the number of components K while searching for the optimal set of mixture parameters H.…”

Section: Related Researchmentioning

confidence: 99%

A new random approach for initialization of the multiple restart EM algorithm for Gaussian model-based clustering

Kwedlo

2015

Pattern Anal Applic

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The paper proposes a new method for initialization of the multiple restart EM algorithm for Gaussian mixture model-based clustering. The method initializes randomly both the mean vector and covariance matrix of a mixture component. In particular, the mean vector is initialized by a feature vector selected deterministically from a random subset of candidate feature vectors. The selection criterion is the maximum Mahalanobis distance from the already initialized mixture component centers. The covariance matrix of a component is initialized by randomly generating its eigenvalues and eigenvectors. In computational experiments, the used approach was compared with three other random EM initialization methods. The experiments were performed on synthetic datasets generated from the Gaussian mixtures with the different overlap characteristics, as well as on four real-life datasets. The results on synthetic data indicate that, for well separated clusters, for which the maximum pairwise overlap is not excessively high, the described method yields clusterings which correspond better to the original partitions of data, as indicated by the adjusted Rand index. The experiments on real data indicate that the performance of the method is comparable to other three methods for two smaller datasets and significantly better for two larger datasets.Keywords Gaussian mixture models Á EM algorithm initialization Á Model-based clustering Á Multiple restart EM

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Section: Related Researchmentioning

confidence: 99%

A new random approach for initialization of the multiple restart EM algorithm for Gaussian model-based clustering

Kwedlo

2015

Pattern Anal Applic

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“…As the C passes its peak value, which is detected as its value decreases in the next iteration, we merge the two Gaussians as in [25].…”

Section: Stochastic Exploration Initialization Approachmentioning

confidence: 99%

“…Variational Bayesian methods avoid overfitting but only provide an approximate solution while Stochastic methods are computationally very expensive. Moreover there are two types of EM based methods in which the number of components need not to be fixed in advance: Firstly divisive where the estimate starts from a single component which split into multiple components as the algorithm proceeds [3,4], [25] and secondly agglomerative where the estimate starts from a large number of components which are decreased as the algorithm proceeds [7,8]. A variety of ways have been proposed for spliting or merging GMM components [3], [14], [22], [24,25].…”

Section: Introductionmentioning

confidence: 99%

A Componentwise Simulated Annealing EM Algorithm for Mixtures

Pervez

Lee

2015

KI 2015: Advances in Artificial Intelligence

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Abstract. This paper addresses the problem of fitting finite Gaussian Mixture Model (GMM) with unknown number of components to the univariate and multivariate data. The typical method for fitting a GMM is Expectation Maximization (EM) in which many challenges are involved i.e. how to initialize the GMM, how to restrict the covariance matrix of a component from becoming singular and setting the number of components in advance. This paper presents a simulated annealing EM algorithm along with a systematic initialization procedure by using the principals of stochastic exploration. The experiments have demonstrated the robustness of our approach on different datasets.

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“…We choose to use the L*u*v* color space for segmentation as in [6,7]. In our case the image color space is represented by a mixture of GMM components.…”

Section: Color Image Segmentationmentioning

confidence: 99%

“…EM has been applied for color image segmentation [6] together with other maximum log-likelihood approaches such as mean shift analysis [7]. In this paper we present a variational approach for color image segmentation.…”

Section: Introductionmentioning

confidence: 99%