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Augmented classical least squares multivariate spectral analysis

  • US 20040064259A1
  • Filed: 09/11/2003
  • Published: 04/01/2004
  • Est. Priority Date: 08/01/2001
  • Status: Active Grant
First Claim
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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)

    1
    CTA=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 K~^;



    and b) predicting a set of component values C~^

    for a prediction set of multivariate spectral data AP by;

    i) further augmenting the augmented pure-component spectra 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 C~^

    using the further augmented pure-component spectra K~^

    according to C~^=AP

    K~^T

    (K~^

    K~^T
    )
    -1
    =AP

    (K~^T)
    +
    .

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