Orthogonal projections and calibration, 20 avril 2012

… Les séminaires ITAP …

Vendredi 20 avril à 10h.Irstea, Bât. Minéa, Salle Orient.

Orthogonal projections and calibration – A review of what the orthogonalization can provide

Jean-Claude Boulet (INRA Montpellier, SPO – Sciences pour l’Oenologie) , Jean-Michel Roger (Irstea, Itap)

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Classical statistics currently uses the orthogonal projection to split the variance into complementary parts. To do that, the projection is performed in the row space (same dimension as number of samples). This operation is found (implicitly) in most of the multivariate linear methods, as PCA, PLS, LDA, etc. and also explicitely in the NIPALS algorithm.
When the variables are (more or less) independent, the orthogonal projection in the column space (same dimension as number of variables) has no evident interest; this is why this option has not been studied in the framework of classical statistics.
When the variables are very dependent, as it is the case in spectrometry, the column space is structured. The useful information lies on a small subspace (comparatively to whole space), as the useless information does. Hence, it becomes useful to clearly separate the useful subspace from the useless one. Calibration intends to identify the useful subspace, spanned by so called latent variables and to focus on it. On the opposite, preprocessing is used to remove the useless information. In the latter situation, the orthogonal projection can provide the chemometrician with efficient tools to improve the calibration model robustness.
Some examples will be shown and discussed. Among them, a pedagogic example will show the efficiency of the orthogonal projection on a PCA of NIR spectra. The interest of orthogonal projection will then be illustrated through the main « orthogonal correction preprocessing » methods, as EPO (external parameter orthogonalisation), TOP (transfer by orthogonal projection), DOP (dynamic orthogonal projection), IDC (improved direct calibration). Some perspective will be given concerning new calibration methods.

 


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