Skip to contents

Projected Orthogonal Signal Correction

Source: R/projected_osc.R
projected_osc.Rd

The projected orthogonal signal correction (POSC) method is a preprocessing technique used to remove systematic variation from predictor variables that is orthogonal to the response variable. This function implements the POSC algorithm for model fitting and prediction.

Usage

projected_osc(
  x,
  y,
  ncomp = 4,
  center = TRUE,
  scale = FALSE,
  tol = 1e-10,
  newdata = NULL
)

Arguments

x

A matrix or data frame of the predictor variables.

y

A vector of the response variable.

ncomp

An integer specifying the number of orthogonal components removed (at least 1), as in the other orthogonalization methods. The underlying PLS model has ncomp + 1 components. Default is 4.

center

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

scale

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

tol

A numeric value; orthogonal components whose singular value is smaller than tol times the largest one are discarded. The default value is 1e-10.

newdata

An optional matrix or data frame of new predictor variables to be corrected using the POSC model. It is preprocessed with the centers and scales of x.

Value

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

  • correction: The corrected x.

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

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

  • weights: The orthogonal weights \(\textbf{W}_o\), such that \(\textbf{T}_o = \textbf{XW}_o\).

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

  • newdata: If newdata is provided, a list with the corrected new data (correction) and its orthogonal scores (scores).

Details

POSC obtains OPLS-filtered data directly from an ordinary (non-orthogonalized) PLS1 model (Kemsley and Tapp, 2009):

  1. A PLS1 model with ncomp + 1 components is fitted, giving the score matrix \(\textbf{T}\) and the fitted response \(\hat{\textbf{y}}\).

  2. The part of the score space orthogonal to \(\hat{\textbf{y}}\), \(\textbf{T} - \hat{\textbf{y}}(\hat{\textbf{y}}^T\hat{\textbf{y}})^{-1}\hat{\textbf{y}}^T\textbf{T}\), spans ncomp orthogonal components with scores \(\textbf{T}_o\).

  3. The orthogonal loadings are \(\textbf{P}_o = \textbf{X}^T\textbf{T}_o(\textbf{T}_o^T\textbf{T}_o)^{-1}\) and the filtered data are \(\textbf{X} - \textbf{T}_o\textbf{P}_o^T\).

The filtered data are identical to those obtained from an OPLS model with one predictive and ncomp orthogonal components (opls() with the same ncomp).

References

  • Kemsley, E.K., Tapp, H.S., (2009). OPLS filtered data can be obtained directly from non-orthogonalized PLS1. Journal of Chemometrics, 23(5):263-264.

  • Trygg, J., Wold, S., (2002). Orthogonal projections to latent structures (O-PLS). Journal of Chemometrics, 16(3):119-128.

See also

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

Author

Christian L. Goueguel

Examples

data(forageLIBS)
spectra <- forageLIBS[-(1:14)]  # the spectral channels
cal <- 1:300
res <- projected_osc(spectra[cal, ], forageLIBS$K[cal], ncomp = 2, newdata = spectra[-cal, ])
dim(res$newdata$correction)
#> [1]   68 7152