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Orthogonal Signal Correction

Source: R/osc.R
osc.Rd

This function implements three orthogonal signal correction (OSC) algorithms, which are a class of preprocessing techniques designed to minimize, in a set of spectral data, the systematic variability or noise not directly related to or correlated with the response vector or property of interest.

Usage

osc(
  x,
  y,
  method = "sjoblom",
  center = TRUE,
  scale = FALSE,
  ncomp = 10,
  tol = 0.001,
  max.iter = 10,
  pls.ncomp = 5
)

Arguments

x

A matrix or data frame of the predictor variables.

y

A vector (or one-column matrix/data frame) of the response variable.

method

A character string indicating the OSC method to use. Accepted values are "wold", "sjoblom" and "fearn". Default is "sjoblom".

center

A logical value indicating whether to mean-centered x and y. Default is TRUE.

scale

A logical value indicating whether to scale x and y. Default is FALSE.

ncomp

An integer representing the number of orthogonal components to remove. Default value is 10; it is reduced to min(n - 1, p) if larger.

tol

A numeric value representing the tolerance for convergence. The default value is 1e-3.

max.iter

An integer representing the maximum number of iterations. The default value is 10.

pls.ncomp

An integer giving the number of PLS components used to compute the weights in Wold's method. Default is 5.

Value

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

  • correction: The corrected matrix.

  • scores: The orthogonal scores matrix.

  • loadings: The orthogonal loadings matrix.

  • weights: The orthogonal weights matrix.

  • R2: The percentage of the (preprocessed) variance of x remaining after correction.

  • angle: The mean angle (in degrees) between the orthogonal scores and y; values close to 90 indicate orthogonality.

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

Details

The OSC algorithm identifies and removes the orthogonal variation in the input spectral matrix, \(\textbf{X}\), by iteratively deflating \(\textbf{X}\) with respect to the response vector \(\textbf{y}\). The resulting \(\textbf{X}\)-matrix contains only the variation that is relevant to the \(\textbf{y}\)-vector, which can then be used for further modeling or analysis. This function implements three different methods for OSC:

  • "wold": the original method of Wold et al. (1998). The first principal component score is orthogonalized to \(\textbf{y}\) and the weights are obtained by a PLS regression of the orthogonalized score on \(\textbf{X}\), iterating until convergence.

  • "sjoblom": the method of Sjöblom et al. (1998), where the weights are obtained by a simple least-squares regression instead of PLS.

  • "fearn": the non-iterative method of Fearn (2000), which finds the directions of maximum variance of \(\textbf{X}\) subject to the scores being exactly orthogonal to \(\textbf{y}\).

For the iterative methods, \(\textbf{X}\) is deflated after each component. New data can be corrected by applying the returned center and scale and then, for each component \(i\), computing \(\textbf{t}_i = \textbf{X}_{new}\textbf{w}_i\) and \(\textbf{X}_{new} \leftarrow \textbf{X}_{new} - \textbf{t}_i\textbf{p}_i^T\).

References

  • Sjöblom, J., Svensson, O., Josefson, M., Kullberg, H., Wold, S., (1998). An evaluation of orthogonal signal correction applied to calibration transfer of near infrared spectra. Chemometrics Intell. Lab. Syst., 44(1):229-244.

  • Fearn, T., (2000). On orthogonal signal correction. Chemometrics Intell. Lab. Syst., 50(1):47-52.

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

  • Svensson, O., Kourti, T. and MacGregor, J.F., (2002). An investigation of orthogonal correction algorithms and their characteristics. Journal of Chemometrics, 16(1):176-188.

See also

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

Author

Christian L. Goueguel

Examples

data(forageLIBS)
spectra <- forageLIBS[-(1:14)]
wl <- as.numeric(names(spectra))
x <- spectra[wl > 760 & wl < 780]  # the K I resonance lines
res <- osc(x, forageLIBS$K, method = "fearn", ncomp = 2)
res$angle
#> [1] 90