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Direct Orthogonalization

Source: R/direct_orthogonal.R
direct_orthogonal.Rd

This function implements the Direct Orthogonalization (DO) algorithm, as proposed by Andersson (1999), to filter out variation from predictor variables, \(\textbf{X}\), that is orthogonal to the response variable(s), \(\textbf{Y}\).

Usage

direct_orthogonal(x, y, ncomp = 2, center = TRUE, scale = FALSE)

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 principal components to retain for orthogonal processing. Default is 2. Values larger than the rank of the orthogonalized matrix are reduced accordingly.

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.

Value

An object of class specproc_direct_orthogonal (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 \(\textbf{XP}\).

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

Details

Contrary to the Orthogonal Signal Correction (OSC) algorithm, Wold et al. (1998), which uses inverse Partial Least Squares (PLS) regression to filter out the orthogonal signal, DO filters out the orthogonal signal directly by orthogonalization of the \(\textbf{X}\) matrix: $$\textbf{Z} = \textbf{X} - \textbf{Y}(\textbf{Y}^T\textbf{Y})^{-1}\textbf{Y}^T\textbf{X}$$ Principal Components Analysis (PCA) is performed on \(\textbf{Z}\) to obtain the loadings \(\textbf{P}\), and the corrected matrix is \(\textbf{X}_{DO} = \textbf{X} - \textbf{XPP}^T\). Direct Orthogonalization is typically simpler and faster than OSC.

To correct new data, preprocess it with the returned center and scale vectors and apply \(\textbf{X}_{new} - \textbf{X}_{new}\textbf{PP}^T\).

References

  • Andersson, C.A., (1999). Direct orthogonalization. Chemometrics Intell. Lab. Syst., 47(1):51-63

  • Pierna, J.A.F., Massart, D.L., de Noord, O.E., Ricoux, P., (2001). Direct orthogonalization: some case studies. Chemometrics Intell. Lab. Syst., 55(1-2):101-108

  • 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, step_direct_orthogonal() to use it in a tidymodels recipe. Before specProc 0.4.0, nas() returned the same correction; it now computes the net analyte signal and figures of merit.

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