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Gaussian Parsimonious Clustering Models Scale Invariant and Stable by Projection

Christophe Biernacki 1 Alexandre Lourme 1 
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 : Gaussian mixture model-based clustering is now a standard tool to determine an hypothetical underlying structure into continuous data. However many usual parsimonious models, despite their appealing geometrical interpretation, suffer from major drawbacks as scale dependence or unsustainability of the constraints by projection. In this work we present a new family of parsimonious Gaussian models based on a variance-correlation decomposition of the covariance matrices. These new models are stable by projection into the canonical planes and, so, faithfully representable in low dimension. They are also stable by modification of the measurement units of the data and such a modification does not change the model selection based on likelihood criteria. We highlight all these stability properties by a specific geometrical representation of each model. A detailed GEM algorithm is also provided for every model inference. Then, on biological and geological data, we compare our stable models to standard geometrical ones.
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https://hal.inria.fr/hal-00688250
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Submitted on : Tuesday, April 17, 2012 - 10:52:07 AM
Last modification on : Wednesday, March 23, 2022 - 3:51:05 PM
Long-term archiving on: : Wednesday, July 18, 2012 - 2:25:50 AM

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  • HAL Id : hal-00688250, version 1

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Christophe Biernacki, Alexandre Lourme. Gaussian Parsimonious Clustering Models Scale Invariant and Stable by Projection. Statistics and Computing, Springer Verlag (Germany), 2013, pp.21. ⟨hal-00688250⟩

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