eposvd {rchemo}

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)

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.

Value

M

orthogonalization matrix.

P

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