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The Mixture Model-based approach

The Mixture Model-based approach. For multivariate data of a continuous nature, attention has focussed on the use of multivariate normal components because of their computational convenience.

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The Mixture Model-based approach

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  1. The Mixture Model-based approach • For multivariate data of a continuous nature, attention has focussed on the use of multivariate normal components because of their computational convenience. • They can be easily fitted iteratively by maximum likelihood (ML) via the expectation-maximization (EM) algorithm (DLR (1977), McLachlan and Krishnan (1997)), as the iterates on the M-step are given in closed form. • In cluster analysis where a mixture model-based approach is widely adopted, the clusters in the data are often essentially elliptical in shape, so that it is reasonable to consider fitting mixtures of elliptically symmetric component densities. Within this class of component densities, the multivariate normal density is a convenient choice given its above-mentioned computational tractability.

  2. Software • The EMMIX software is used for the fitting of the mixture of three normal components, • The EMMIX algorithm has several options, including the option to carry out a resampling-based test for the number of components in the mixture model.

  3. MODEL-BASED ML CLUSTERING ANALYSIS • The goals are to determine the cluster assignment of each element and to estimate the mean mk and covariance matrix Sk for each cluster. • We assume that the population consists of a mixture of multivariate Gaussian classes. • In the model considered the nth-dimensional observations Xi are drawn from g multinormal groups, each of which is characterized by a vector of parameters Qk for k=1,2,3

  4. RESULTS Durations Fluence Spectrum Short/faint/hard Long/interm/bright Interm/interm/soft Class III Class II Class I

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