Metrohm Vision – Theory - Manual (Page 23)

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5
Identification and Qualification Methods
5.1 Wavelength Correlation
5.1.1 Model Development
The first step in development of a wavelength correlation model is the calculation of a mean
spectrum for every product in the training set. Every sample spectrum for a product is used in the
calculation of the mean spectrum for that product.
5.1.2 Analysis of an Unknown
The correlation between an unknown spectrum and every mean product spectrum is calculated. The
unknown is identified as that product for which the correlation value is above the threshold value.
The default thresholds are 0.84 for identification and 0.9 for qualification.
5.2 Wavelength Maximum Distance
5.2.1 Model Development
The first step in development of a wavelength correlation model is the calculation of a mean
spectrum for every product in the training set. Every sample spectrum for a product is used in the
calculation of the mean spectrum for that product.
5.2.2 Analysis of an Unknown
The maximum distance between an unknown spectrum and every mean product spectrum is
calculated. The unknown is identified as that product for which the correlation value is below the
threshold value. Default thresholds are 4 for identification and 3 for qualification.
5.3 Mahalanobis Distance in Principal Component Space
Library identification based on Mahalanobis distance calculates a local Principal Component model
for each product in the library. Then a qualification method is developed separately for each product.
5.3.1 Model Development
Principal Component Analysis performed on the training set of spectra of a given product yields a set
of eigenvectors with corresponding eigenvalues. From the cumulative variance threshold defined for
the model, the number of primary PCs in the model is determined. Multiplication of spectra and
eigenvectors yields scores (spectral coordinates in the Principal Component space).
Mahalanobis distances are distributed according to chi-square function. (Chi-square is a statistical
function with well-known properties.) From the chi-square function one can calculate probability
that a given sample belongs to the distribution represented by the training set.
The Mahalanobis distance method offers a choice of two types of thresholds : probability or match
value. Threshold expressed as probability is the recommended type. Vision has built-in probability
function based on the chi-square distribution. Samples’ Mahalanobis distances and the number of
degrees of freedom of the training set are passed to this function, which returns a probability that
the sample does not belong to the distribution represented by the training set of spectra (1-α).