BUCHI NIRCal - Manual (Page 182)

NIRCal 5.5 Software Manual
182 NIRCal 5.5 Manual, Version A
The spectra are internal for the Durbin-Watson calculation ascending sorted according the original
property values of each properties. By the same property values the original sequence will be kept.
C-Set / V-Set : the dw will be calculated separately. If the V-Set is empty dw = 2 protocoled.
Durbin-Watson test is available in NIRCal:

the calibration protocol of quantitative calibration has the dw value for C-Set and V-Set;

the dw values are in the matrices.
3.18.41 Eigenvalue
Description Corresponding Eigenvalues for PCs and scores.
Use To select the number of primary PCs.
Method PCR / PLS / Cluster (CLU) / SIMCA
Matrices ID 5
Tip The eigenvalue matrix is in diagonal form.
Details High eigenvalue describes high spectral influence.
Related Topic Scores , Primary PCs , Loadings
Eigenvalue gives the information about the importance of the PCs: high value means high information,
small value indicates less information.
Explanation of mathematical correlation of the loadings and eigenvalue using Mahalanobis distance of
the PCA (PCR, CLU, SIMCA):
where:

F factor / loadings matrix

F` transposed factor / loadings matrix;

eigenvalue

L scores matrix;

L` transposed score matrix;

I identity matrix (diagonal matrix with 1).
The equation of the spectra reconstruction using this terminology:
This is equivalent to the equation given by the Loadings (links) explanation.
The results are different using Mahalanobis or Euclidean distance:
Mahalanobis Euclidean
FF
' Diagonal matrix with eigenvalue Diagonal matrix with 1
LL
' Diagonal matrix with 1 Diagonal matrix with eigenvalue
The calculation of eigenvalue is different by the PLS method: the eigenvalue are calculated under
consideration of the property value variance. Therefore iterative algorithms, like nipals, are used.