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Normal mixture models are widely used for statistical modeling of data, including cluster analysis.
However maximum likelihood estimation (MLE) for normal mixtures using the EM algorithm may fail as the result of singularities
or degeneracies. To avoid this, we propose replacing the MLE by a maximum a posteriori (MAP) estimator, also found by the
EM algorithm. For choosing the number of components and the model parameterization, we propose a modified version of BIC,
where the likelihood is evaluated at the MAP instead of the MLE. We use a highly dispersed proper conjugate prior, containing
a small fraction of one observation's worth of information. The resulting method avoids degeneracies and singularities, but
when these are not present it gives similar results to the standard method using MLE, EM and BIC. 相似文献
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Fionn Murtagh 《Journal of Classification》2009,26(3):249-277
An ultrametric topology formalizes the notion of hierarchical structure. An ultrametric embedding, referred to here as ultrametricity,
is implied by a hierarchical embedding. Such hierarchical structure can be global in the data set, or local. By quantifying
extent or degree of ultrametricity in a data set, we show that ultrametricity becomes pervasive as dimensionality and/or spatial
sparsity increases. This leads us to assert that very high dimensional data are of simple structure. We exemplify this finding
through a range of simulated data cases. We discuss also application to very high frequency time series segmentation and modeling. 相似文献