epo: External parameter orthogonalization (EPO)

In mlesnoff/rchemo: Dimension reduction, Regression and Discrimination for Chemometrics

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.

The data corrected from the detrimental information D can be computed by X_corrected = X * M.

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.

Value

See the examples.

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)    # Detrimental information

nlv <- 2
res <- eposvd(D, nlv = nlv)
M <- res$M       # orthogonalization matrix
P <- res$P       # detrimental directions matrix (loadings of D = columns of P)
M
P

## The matrix corrected from D can be computed by:
## X_corr <- X %*% M    
## Rows of the corrected matrix X_corr
## are orthogonal to the loadings vectors (columns of P):
## X_corr %*% P 

mlesnoff/rchemo documentation built on April 15, 2023, 1:25 p.m.