Gaussian mixture models for the classification of high-dimensional vibrational spectroscopy data

Julien Jacques (1) , Charles Bouveyron (2) , Stéphane Girard (3) , Olivier Devos (4) , Ludovic Duponchel (4) , Cyril Ruckebusch (4)

1 LPP - Laboratoire Paul Painlevé - UMR 8524
2 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
3 MISTIS - Modelling and Inference of Complex and Structured Stochastic Systems
4 LASIRE - Laboratoire Avancé de Spectroscopie pour les Intéractions la Réactivité et l'Environnement - UMR 8516

In this work, a family of generative Gaussian models designed for the supervised classification of high-dimensional data is presented as well as the associated classification method called High Dimensional Discriminant Analysis (HDDA). The advantages of these Gaussian models are: i) the representation of the input density model is smooth; ii) the data of each class are modeled in a specific subspace of low dimensionality; iii) each class may have its own covariance structure; iv) regularization is coupled to the classification criterion to avoid data over-fitting. To illustrate the abilities of the method, HDDA is applied on complex high-dimensional multi-class classification problems in mid-infrared and near infrared spectroscopy and compared to state-of-the-art methods.

Mots clés: Model-based classification; High-dimensional gaussian model; Generative model; Vibrational spectroscopy

Domaines: Statistiques [math.ST]; Théorie [stat.TH]

Julien Jacques, Charles Bouveyron, Stéphane Girard, Olivier Devos, Ludovic Duponchel, et al.. Gaussian mixture models for the classification of high-dimensional vibrational spectroscopy data. Journal of Chemometrics, 2010, 24 (11-12), pp.719-727. ⟨10.1002/cem.1355⟩. ⟨hal-00459947v2⟩