Augmented classical least squares multivariate spectral analysis
First Claim
1. A method for analyzing multivariate spectral data, comprising the steps of:
- a) creating a calibration model for a calibration set of multivariate spectral data A by;
i) obtaining a set of reference component values C representative of at least one of the spectrally active components in the calibration set of multivariate spectral data A, ii) estimating pure-component spectra {circumflex over (K)} for the at least one of the spectrally active components according to {circumflex over (K)}=(CTC)−
1CTA=C+A, iii) obtaining spectral residuals EA according to EA=A−
C{circumflex over (K)}, and iv) augmenting the estimated pure-component spectra {circumflex over (K)} with at least one vector of the spectral residuals EA to obtain augmented pure-component spectra {tilde over ({circumflex over (K)})}; and
b) predicting a set of component values {tilde over ({circumflex over (C)})} for a prediction set of multivariate spectral data AP by;
i) further augmenting the augmented pure-component spectra {tilde over ({circumflex over (K)})} with at least one vector representing a spectral shape that is representative of at least one additional source of spectral variation in the prediction set, and ii) predicting the set of component values {tilde over ({circumflex over (C)})} using the further augmented pure-component spectra {tilde over ({circumflex over (K)})} according to {tilde over ({circumflex over (C)})}=AP{tilde over ({circumflex over (K)})}T({tilde over ({circumflex over (K)})}{tilde over ({circumflex over (K)})}T)−
1=AP({tilde over ({circumflex over (K)})}T)+.
3 Assignments
0 Petitions
Accused Products
Abstract
A method of multivariate spectral analysis, termed augmented classical least squares (ACLS), provides an improved CLS calibration model when unmodeled sources of spectral variation are contained in a calibration sample set. The ACLS methods use information derived from component or spectral residuals during the CLS calibration to provide an improved calibration-augmented CLS model. The ACLS methods are based on CLS so that they retain the qualitative benefits of CLS, yet they have the flexibility of PLS and other hybrid techniques in that they can define a prediction model even with unmodeled sources of spectral variation that are not explicitly included in the calibration model. The unmodeled sources of spectral variation may be unknown constituents, constituents with unknown concentrations, nonlinear responses, non-uniform and correlated errors, or other sources of spectral variation that are present in the calibration sample spectra. Also, since the various ACLS methods are based on CLS, they can incorporate the new prediction-augmented CLS (PACLS) method of updating the prediction model for new sources of spectral variation contained in the prediction sample set without having to return to the calibration process. The ACLS methods can also be applied to alternating least squares models. The ACLS methods can be applied to all types of multivariate data.
-
Citations
24 Claims
-
1. A method for analyzing multivariate spectral data, comprising the steps of:
-
a) creating a calibration model for a calibration set of multivariate spectral data A by;
i) obtaining a set of reference component values C representative of at least one of the spectrally active components in the calibration set of multivariate spectral data A, ii) estimating pure-component spectra {circumflex over (K)} for the at least one of the spectrally active components according to {circumflex over (K)}=(CTC)−
1CTA=C+A,iii) obtaining spectral residuals EA according to EA=A−
C{circumflex over (K)}, andiv) augmenting the estimated pure-component spectra {circumflex over (K)} with at least one vector of the spectral residuals EA to obtain augmented pure-component spectra {tilde over ({circumflex over (K)})}; and
b) predicting a set of component values {tilde over ({circumflex over (C)})} for a prediction set of multivariate spectral data AP by;
i) further augmenting the augmented pure-component spectra {tilde over ({circumflex over (K)})} with at least one vector representing a spectral shape that is representative of at least one additional source of spectral variation in the prediction set, and ii) predicting the set of component values {tilde over ({circumflex over (C)})} using the further augmented pure-component spectra {tilde over ({circumflex over (K)})} according to {tilde over ({circumflex over (C)})}=AP{tilde over ({circumflex over (K)})}T({tilde over ({circumflex over (K)})}{tilde over ({circumflex over (K)})}T)−
1=AP({tilde over ({circumflex over (K)})}T)+.- View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12)
-
-
13. A method for analyzing multivariate spectral data, comprising the steps of:
-
a) creating a calibration model for a calibration set of multivariate spectral data A by;
i) obtaining a set of reference component values C representative of at least one of the spectrally active components in the calibration set of multivariate spectral data A, ii) estimating pure-component spectra {circumflex over (K)} for the at least one of the spectrally active components according to {circumflex over (K)}=(CTC)−
1CTA=C+A,iii) obtaining spectral residuals EA according to EA=A−
C{circumflex over (K)},iv) decomposing the spectral residuals EA according to EA=TP+E where T is a set of n×
r scores and P is a set of r×
p loading vectors obtained from factor analysis of the spectral residuals EA, and E is a set of n×
p random errors and spectral variations not useful for prediction,v) augmenting the set of reference component values C with at least one vector of the T scores to obtain a set of augmented component values {tilde over (C)}, and vi) estimating augmented pure-component spectra {tilde over ({circumflex over (K)})} according to {tilde over ({circumflex over (K)})}=({tilde over (C)}T{tilde over (C)})−
1{tilde over (C)}TA≈
{tilde over (C)}+A; and
b) predicting a set of component values {tilde over ({circumflex over (C)})} for a prediction set of multivariate spectral data AP according to {tilde over ({circumflex over (C)})}=AP{tilde over ({circumflex over (K)})}T({tilde over ({circumflex over (K)})}{tilde over ({circumflex over (K)})}T)−
1=AP({tilde over ({circumflex over (K)})}T)+.- View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24)
-
Specification