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An efficient SEM algorithm for Gaussian Mixtures with missing data

Vincent Vandewalle 1, 2 C Biernacki 1, 3 
1 MODAL - MOdel for Data Analysis and Learning
LPP - Laboratoire Paul Painlevé - UMR 8524, Université de Lille, Sciences et Technologies, Inria Lille - Nord Europe, METRICS - Evaluation des technologies de santé et des pratiques médicales - ULR 2694, Polytech Lille - École polytechnique universitaire de Lille
Abstract : The missing data problem is well-known for statisticians but its frequency increases with the growing size of modern datasets. In Gaussian model-based clustering, the EM algorithm easily takes into account such data by dealing with two kinds of latent levels: the components and the variables. However, the quite familiar degeneracy problem in Gaussian mixtures is aggravated during the EM runs. Indeed, numerical experiments clearly reveal that degeneracy is quite slow and also more frequent than with complete data. In practice, such situations are difficult to detect efficiently. Consequently, degenerated solutions may be confused with valuable solutions and, in addition, computing time may be wasted through wrong runs. A theoretical and practical study of the degeneracy will be presented. Moreover a simple condition on the latent partition to avoid degeneracy will be exhibited. This condition is used in a constrained version of the Stochastic EM (SEM) algorithm. Numerical experiments on real and simulated data illustrate the good behaviour of the proposed algorithm.
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https://hal.inria.fr/hal-01242588
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Submitted on : Monday, December 14, 2015 - 3:56:14 PM
Last modification on : Wednesday, March 23, 2022 - 3:51:09 PM

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  • HAL Id : hal-01242588, version 1

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Vincent Vandewalle, C Biernacki. An efficient SEM algorithm for Gaussian Mixtures with missing data. 8th International Conference of the ERCIM WG on Computational and Methodological Statistics, Dec 2015, Londres, United Kingdom. ⟨hal-01242588⟩

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