, ? Modélisation physique d'un spectre à partir d'un modèle de réectance surfacique

. ?-a-partir,

, Génération de n = 12.000 spectres synthétiques (accompagnés de leurs paramètres physiques associés)

, ? Estimation de la relation fonctionnelle inverse Y = G(X)

, Hypothèse de réduction de dimension G(X) = g(b t X)

, ? b est estimé par SIR, g est estimé par régression nonparamétrique unidimensionnelle

, Taille des grains de glace de CO 2 estimée par SIR à partir d'une image hyperspectrale de la planète Mars. References

R. , The scree test for the number of factors, Multivariate Behavioral Research, vol.1, issue.2, p.245276, 1966.

K. Li, Sliced inverse regression for dimension reduction, Journal of the American Statistical Association, 1991.
DOI : 10.2307/2290563

D. Scott and J. Thompson, Probability density estimation in higher dimensions, Fifteenth Symposium in the Interface, p.173179, 1983.

G. Schwarz, Estimating the dimension of a model, The Annals of Statistics, vol.6, p.461464, 1978.

C. Bouveyron, S. Girard, and C. Schmid, High dimensional data clustering, Computational Statistics and Data Analysis, vol.52, p.502519, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00548573

C. Bouveyron, S. Girard, and C. Schmid, High dimensional discriminant analysis, Communication in Statistics -Theory and Methods, vol.36, issue.14, p.26072623, 2007.
URL : https://hal.archives-ouvertes.fr/inria-00548516

J. Jacques, C. Bouveyron, S. Girard, O. Devos, L. Duponchel et al., Gaussian mixture models for the classication of high-dimensional vibrational spectroscopy data, Journal of Chemometrics, vol.24, p.719727, 2010.

C. Bouveyron, G. Celeux, and S. Girard, Intrinsic dimension estimation by maximum likelihood in isotropic probabilistic PCA, Pattern Recognition Letters, vol.32, issue.14, p.17061713, 2011.
DOI : 10.1016/j.patrec.2011.07.017
URL : https://hal.archives-ouvertes.fr/hal-00440372

C. Bouveyron, M. Fauvel, and S. Girard, Kernel discriminant analysis and clustering with parsimonious Gaussian process models, Statistics and Computing, vol.25, p.11431162, 2015.
DOI : 10.1007/s11222-014-9505-x
URL : https://hal.archives-ouvertes.fr/hal-00707056

C. Bernard-michel, L. Gardes, and S. Girard, Gaussian regularized sliced inverse regression, Statistics and Computing, vol.19, p.8598, 2009.
DOI : 10.1007/s11222-008-9073-z
URL : https://hal.archives-ouvertes.fr/inria-00180458

C. Bernard-michel, L. Gardes, and S. Girard, A note on sliced inverse regression with regularizations, Biometrics, vol.64, p.982986, 2008.
URL : https://hal.archives-ouvertes.fr/inria-00180496

C. Bernard-michel, S. Douté, M. Fauvel, L. Gardes, and S. Girard, Retrieval of Mars surface physical properties from Omega hyperspectral images using regularized sliced inverse regression, Journal of Geophysical Research -Planets, vol.114, 2009.
URL : https://hal.archives-ouvertes.fr/inria-00276116

M. Chavent, S. Girard, V. Kuentz, B. Liquet, T. M. Nguyen et al., A sliced inverse regression approach for data stream, Computational Statistics, vol.29, p.11291152, 2014.
DOI : 10.1007/s00180-014-0483-4
URL : https://hal.archives-ouvertes.fr/hal-01139870

R. Coudret, S. Girard, and J. Saracco, A new sliced inverse regression method for multivariate response, Computational Statistics and Data Analysis, vol.77, p.285299, 2014.
DOI : 10.1016/j.csda.2014.03.006
URL : https://hal.archives-ouvertes.fr/hal-00714981

A. Chiancone, F. Forbes, and S. Girard, Student sliced inverse regression, Computational Statistics and Data Analysis, vol.113, p.441456, 2017.
DOI : 10.1016/j.csda.2016.08.004
URL : https://hal.archives-ouvertes.fr/hal-01415576