2022
DOI: 10.1007/s11634-021-00488-x
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Gaussian mixture model with an extended ultrametric covariance structure

Abstract: Gaussian Mixture Models (GMMs) are one of the most widespread methodologies for model-based clustering. They assume a multivariate Gaussian distribution for each component of the mixture, centered at the mean vector and with volume, shape and orientation derived by the covariance matrix. To reduce the large number of parameters produced by the covariance matrices, parsimonious parameterizations of the latter were proposed in literature, e.g., the eigen-decomposition and the parsimonious GMMs based on mixtures … Show more

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Cited by 6 publications
(2 citation statements)
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“…The resulting sparse representation may allow otherwise computationally infeasible and standard manipulations of these matrices, such as inverting and factoring them and characterizing their spectrum and eigenvectors. Noteworthily, our results generalize to the class of extended ultrametric covariance matrices and hence may find application in the parameterization of covariance matrices of Gaussian mixture models [16].…”
Section: Discussionmentioning
confidence: 98%
See 1 more Smart Citation
“…The resulting sparse representation may allow otherwise computationally infeasible and standard manipulations of these matrices, such as inverting and factoring them and characterizing their spectrum and eigenvectors. Noteworthily, our results generalize to the class of extended ultrametric covariance matrices and hence may find application in the parameterization of covariance matrices of Gaussian mixture models [16].…”
Section: Discussionmentioning
confidence: 98%
“…The sparsification achieved by these wavelets can be substantial in large, ultrametric matrices, which would otherwise be inaccessible due to their size. These sparse representations can be valuable in phylogenetic applications [3], network inference [4] and hierarchical clustering problems [12,16] as their models often rely on tree-structured covariance matrices.…”
Section: Introductionmentioning
confidence: 99%