Piecewise Direct Standardization

The pds function performs Piecewise Direct Standardization (PDS), a method proposed by Wang et al. (1991) to transfer spectra from one instrument to another. Optionally, the local models can be blended with a global PLSR model (direct standardization), which can lead to better transfer performance when the instrumental differences are not purely local.

Usage

pds(x1, x2, win = 5, ncomp = 2, alpha = 0)

Arguments

x1

A matrix or data frame containing spectra acquired with the standard (master) instrument.

x2

A matrix or data frame containing spectra of the same samples acquired with the instrument to be standardized (slave).

win

An integer specifying the half size of the moving window used for PLSR. A larger value may improve the transfer but will increase computational time. Default is 5.

ncomp

An integer specifying the number of components to be used in PLSR. Typically, a small number (e.g., 2-5) is sufficient. Default is 2.

alpha

A numeric value between 0 and 1 specifying the weight for the global PLSR model. A value of 0 (default) corresponds to the original PDS method, while a value of 1 corresponds to using only the global PLSR model.

Value

A list with two components:

transfer_matrix

The \(p \times p\) transfer matrix \(\textbf{F}\).

intercept

A vector of length \(p\) containing the intercepts.

Details

For each wavelength \(j\) of the standard (master) instrument, a PLSR model is fitted between the response of the master instrument at \(j\) and the responses of the slave instrument in the window \([j - win, j + win]\) (truncated at the edges of the spectrum). The regression coefficients are stored in a banded transfer matrix \(\textbf{F}\), and the intercepts in a vector \(\textbf{b}_0\). Spectra measured on the slave instrument are then standardized as $$\textbf{X}_{2,std} = \textbf{X}_2 \textbf{F} + \textbf{1}\textbf{b}_0^T$$

When alpha > 0, a global PLSR model mapping the whole slave spectrum to the whole master spectrum is also fitted, and the transfer matrix and intercept are \((1 - \alpha)\) times the local ones plus \(\alpha\) times the global ones.

References

• Wang, Y., Veltkamp, D.J., Kowalski, B.R., (1991). Multivariate instrument standardization. Analytical Chemistry, 63(23):2750-2756.

• Bouveresse, E., Massart, D.L., (1996). Improvement of the piecewise direct standardization procedure for the transfer of NIR spectra for multivariate calibration. Chemometrics and Intelligent Laboratory Systems, (32)2:201-213.

Author

Christian L. Goueguel

Examples

data(forageLIBS)
wl <- suppressWarnings(as.numeric(names(forageLIBS)))
spectra <- forageLIBS[which(wl > 760 & wl < 780)]  # the K I resonance lines
# a second instrument, with a shifted and less sensitive response
x1 <- as.matrix(spectra[1:30, ])
x2 <- 0.8 * cbind(x1[, -1], x1[, ncol(x1)]) + 50
res <- pds(x1, x2, win = 3, ncomp = 2)
# spectra of the second instrument transferred to the first one
transferred <- sweep(x2 %*% res$transfer_matrix, 2, res$intercept, "+")
max(abs(transferred - x1)) / max(x1)
#> [1] 0.0313053