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Direct Orthogonal Signal Correction

Source: R/direct_osc.R
direct_osc.Rd

This function implements the Direct Orthogonal Signal Correction (DOSC) algorithm, as proposed by Westerhuis et al. (2001), to remove systematic variation from predictor variables, \(\textbf{X}\), that is orthogonal to the response variable(s), \(\textbf{Y}\).

Usage

direct_osc(x, y, ncomp = 10, center = TRUE, scale = FALSE, tol = 0.001)

Arguments

x

A matrix or data frame of the predictor variables

y

A vector, matrix or data frame of the response variable(s)

ncomp

An integer specifying the number of orthogonal components to remove. Default is 10; it is reduced if larger than the rank of the orthogonalized matrix.

center

A logical value specifying whether to center the data. Default is TRUE.

scale

A logical value specifying whether to scale the data. Default is FALSE.

tol

A numeric value giving the relative tolerance used to compute the pseudo-inverse of \(\textbf{X}\); singular values smaller than tol times the largest one are discarded, which regularizes the weights. Default is 1e-3.

Value

An object of class specproc_direct_osc (a list), which predict() applies to new spectra, with the following components:

  • correction: The corrected matrix.

  • loading: The loadings matrix \(\textbf{P}\).

  • score: The scores matrix \(\textbf{T}\).

  • weight: The weights matrix \(\textbf{W}\).

  • center, scale: The column centers and scales applied to x.

Details

Different from the Orthogonal Signal Correction (OSC) algorithm, Wold et al. (1998), the DOSC algorithm is non-iterative:

  1. \(\textbf{Y}\) is projected onto the column space of \(\textbf{X}\): \(\hat{\textbf{Y}} = \textbf{XX}^{+}\textbf{Y}\).

  2. \(\textbf{X}\) is orthogonalized with respect to \(\hat{\textbf{Y}}\): \(\textbf{Z} = \textbf{X} - \hat{\textbf{Y}}\hat{\textbf{Y}}^{+}\textbf{X}\).

  3. PCA of \(\textbf{Z}\) gives the orthogonal scores \(\textbf{T}\).

  4. The weights \(\textbf{W} = \textbf{X}^{+}\textbf{T}\) express the scores as a linear combination of \(\textbf{X}\), the loadings are \(\textbf{P} = \textbf{X}^T\textbf{T}(\textbf{T}^T\textbf{T})^{-1}\), and the corrected matrix is \(\textbf{X} - \textbf{TP}^T\).

New data are corrected with \(\textbf{X}_{new} - \textbf{X}_{new}\textbf{WP}^T\) after applying the returned center and scale.

References

  • Westerhuis, J.A., Jong, S.D., Smilde, A.K., (2001). Direct orthogonal signal correction. Chemometrics Intell. Lab. Syst., 56(1):13-25

  • Wold, S., Antti, H., Lindgren, F., Ohman, J. (1998). Orthogonal signal correction of near-infrared spectra. Chemometrics Intell. Lab. Syst., 44(1):175-185.

See also

predict.specproc_filter() to correct new spectra with the fitted filter, and step_direct_osc() to use it in a tidymodels recipe.

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
res <- direct_osc(spectra, forageLIBS$K, ncomp = 2)
dim(res$correction)
#> [1] 368 245