Estimation of gaussian mixtures with rotationally invariant covariance matrices |
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Authors: | R.L. Streit Luginbuhl T. E |
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Affiliation: | Naval Undersea Warfare Center , Newport, RI, 02841-1708, USA |
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Abstract: | Homoscedastic and heteroscedastic Gaussian mixtures differ in the constraints placed on the covariance matrices of the mixture components. A new mixture, called herein a strophoscedastic mixture, is defined by a new constraint, This constraint requires the matrices to be identical under orthogonal trans¬formations, where different transformations are allowed for different matrices. It is shown that the M-step of the EM method for estimating the parameters of strophoscedastic mixtures from sample data is explicitly solvable using singular value decompositions. Consequently, the EM-based maximum likelihood estimation algorithm is as easily implemented for strophoscedastic mixtures as it is for homoscedastic and heteroscedastic mixtures. An example of a “noisy” Archimedian spiral is presented. |
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Keywords: | parameter estimation maximum likelihood EM method strophoscedastic mixtures orthogonal invariance singular value decomposition |
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