Classical least squares multivariate spectral analysis
First Claim
1. A method for performing a classical least squares estimation of the value of at least one source of spectral variation of a sample comprising:
- utilizing a previously constructed calibration data set wherein the constituents of such calibration data set include at least one of the sources of spectral variation that affect the optical response of the sample to be measured, such calibration data set yielding a matrix {circumflex over (K)} representing the combination of the vectors containing the at least one spectral shape of the measured sources of spectral variation;
measuring the optical response of a sample set that contains the at least one of the sources of spectral variation in the calibration data set and at least one additional source of spectral variation whose value was not represented in the original calibration data set, said measurement forming a prediction data set;
adding at least one vector representing a spectral shape that is representative of the at least one additional source of spectral variation in the prediction data set to the matrix {circumflex over (K)} to form an augmented matrix {tilde over ({circumflex over (K)})}; and
estimating the value of the at least one of the sources of spectral variation in the calibration data set or the at least one additional source of spectral variation in the sample by a classical least squares prediction utilizing the augmented matrix {tilde over ({circumflex over (K)})}, wherein the at least one additional source of spectral variation is a non-baseline source of spectral variation.
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Abstract
An improved classical least squares multivariate spectral analysis method that adds spectral shapes describing non-calibrated components and system effects (other than baseline corrections) present in the analyzed mixture to the prediction phase of the method. These improvements decrease or eliminate many of the restrictions to the CLS-type methods and greatly extend their capabilities, accuracy, and precision. One new application of PACLS includes the ability to accurately predict unknown sample concentrations when new unmodeled spectral components are present in the unknown samples. Other applications of PACLS include the incorporation of spectrometer drift into the quantitative multivariate model and the maintenance of a calibration on a drifting spectrometer. Finally, the ability of PACLS to transfer a multivariate model between spectrometers is demonstrated.
92 Citations
30 Claims
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1. A method for performing a classical least squares estimation of the value of at least one source of spectral variation of a sample comprising:
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utilizing a previously constructed calibration data set wherein the constituents of such calibration data set include at least one of the sources of spectral variation that affect the optical response of the sample to be measured, such calibration data set yielding a matrix {circumflex over (K)} representing the combination of the vectors containing the at least one spectral shape of the measured sources of spectral variation;
measuring the optical response of a sample set that contains the at least one of the sources of spectral variation in the calibration data set and at least one additional source of spectral variation whose value was not represented in the original calibration data set, said measurement forming a prediction data set;
adding at least one vector representing a spectral shape that is representative of the at least one additional source of spectral variation in the prediction data set to the matrix {circumflex over (K)} to form an augmented matrix {tilde over ({circumflex over (K)})}; and
estimating the value of the at least one of the sources of spectral variation in the calibration data set or the at least one additional source of spectral variation in the sample by a classical least squares prediction utilizing the augmented matrix {tilde over ({circumflex over (K)})}, wherein the at least one additional source of spectral variation is a non-baseline source of spectral variation. - View Dependent Claims (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15)
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16. A method for estimating a measure of at least one component within a sample including a plurality of components, comprising the steps of:
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a) obtaining a calibration data set A1 composed of first attributes K1 of the plurality of components within a first sample set S1 composed of at least two different samples;
b) obtaining a second data set A2 composed of second attributes K2 of the plurality of components within a second sample set S2, wherein the second sample set S2 includes at least one component not in the first sample set S1;
c) estimating a third attribute K3 of the at least one other component not in the first set S1 of samples and combining it with calibration model from A1 to obtain an augmented set of attributes {tilde over (K)}; and
d) predicting a measure of at least one component in the second sample set S2 according to {tilde over (C)}=({tilde over (K)}T{tilde over (K)})−
1{tilde over (K)}TA≈
{tilde over (K)}A.- View Dependent Claims (17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 30)
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29. A method for estimating a measure of at least one component within a sample including a plurality of components, comprising the steps of:
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a) obtaining a calibration data set A1 composed of first attributes K1 of the plurality of identified components within a first sample set S1 composed of at least two different samples;
b) obtaining a measure EA of unknown variables in the calibration data set A1 and separating EA into coherent P and incoherent E components;
c) augmenting the first set of attributes K1 with at least one coherent P and at least one incoherent E components to obtain an augmented first set of attributes {tilde over (K)}1;
d) obtaining a second data set A2 composed of second attributes K2 of the plurality of components within a second sample set S2, wherein the second sample set S2 includes at least one component not in the first sample set S1;
e) estimating a third attribute K3 of the at least one other component not in the first set S1 of samples and combining it with calibration model from A1 to obtain a second augmented set of attributes {tilde over (K)}2; and
f) predicting a measure of at least one component in the second sample S2 according to {tilde over (C)}=({tilde over (K)}T{tilde over (K)})−
1{tilde over (K)}TA≈
{tilde over (K)}A.
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Specification