Finite mixture models and model-based clustering

Melnykov, Volodymyr; Maitra, Ranjan

doi:10.1214/09-ss053

Cited by 262 publications

(173 citation statements)

References 117 publications

Supporting

Mentioning

162

Contrasting

Unclassified

Order By: Relevance

“…Each iteration j of the algorithm consists of two steps called the expectation step (E-step) and the maximization step (M-step). For GMMs, these steps are defined as follows [27,32]: -E-Step: Given the set of mixture parameters H ðjÀ1Þ from the previous iteration, for each m ¼ 1; . .…”

Section: Em Algorithm For Gaussian Mixture Modelsmentioning

confidence: 99%

“…Mixture models [12,25,27] are very useful tools, widely applied in pattern recognition for modeling complex probability distributions. A finite mixture model pðxjHÞ can be expressed by a weighted sum of K components:…”

Section: Introductionmentioning

confidence: 99%

“…. ; a K g: GMMs are widely used in such applications as data clustering [12,27], data classification [15], speaker recognition [33], image segmentation and classification [29]. Estimation of the parameters of a GMM can be performed using the maximum likelihood approach.…”

Section: Introductionmentioning

confidence: 99%

“…Model-based clustering [12,27] is one of the most important applications of GMMs. The aim of clustering can be defined as dividing a set of objects into K disjoint groups, called clusters, in such a way that the objects within the same group are very similar, whereas the objects in different groups are very distinct.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

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

Kwedlo

2015

Pattern Anal Applic

View full text Add to dashboard Cite

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

show abstract

Section: Em Algorithm For Gaussian Mixture Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Kwedlo

2015

Pattern Anal Applic

View full text Add to dashboard Cite

show abstract

“…Fraley and Raftery 2002) and the Latent Class Analysis model, which is a mixture of products of independent Bernoulli models (Lazarsfeld and Henry 1968). Extensive reviews of mixture models and their application are given in Everitt and Hand (1981), Titterington et al (1985), McLachlan and Basford (1988), McLachlan and Peel (2000), Raftery (1998, 2002) and Melnykov and Maitra (2010).…”

Section: Mixture Modelsmentioning

confidence: 99%