rchemo (version 0.1-3)

eposvd: External parameter orthogonalization (EPO)

Description

Pre-processing a X-dataset by external parameter orthogonalization (EPO; Roger et al 2003). The objective is to remove from a dataset X \((n, p)\) some "detrimental" information (e.g. humidity effect) represented by a dataset \(D (m, p)\).

EPO consists in orthogonalizing the row observations of \(X\) to the detrimental sub-space defined by the first \(nlv\) non-centered PCA loadings vectors of \(D\).

Function eposvd uses a SVD factorization of \(D\) and returns \(M (p, p)\) the orthogonalization matrix, and \(P\) the considered loading vectors of \(D\).

Usage

eposvd(D, nlv)

Value

M

orthogonalization matrix.

P

detrimental directions matrix (p, nlv) (loadings of D = columns of P).

Arguments

D

A dataset \((m, p)\) containing detrimental information.

nlv

The number of first loadings vectors of \(D\) considered for the orthogonalization.

Details

The data corrected from the detrimental information \(D\) can be computed by \(Xcorrected = X * M\). Rows of the corrected matrix Xcorr are orthogonal to the loadings vectors (columns of P): \(Xcorr * P\).

References

Roger, J.-M., Chauchard, F., Bellon-Maurel, V., 2003. EPO-PLS external parameter orthogonalisation of PLS application to temperature-independent measurement of sugar content of intact fruits. Chemometrics and Intelligent Laboratory Systems 66, 191-204. https://doi.org/10.1016/S0169-7439(03)00051-0

Roger, J.-M., Boulet, J.-C., 2018. A review of orthogonal projections for calibration. Journal of Chemometrics 32, e3045. https://doi.org/10.1002/cem.3045

Examples

n <- 4 ; p <- 8 
X <- matrix(rnorm(n * p), ncol = p)
m <- 3
D <- matrix(rnorm(m * p), ncol = p)

nlv <- 2
res <- eposvd(D, nlv = nlv)
M <- res$M
P <- res$P
M
P