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Chemometric methods

Chemometric methods refer to mathematical methods designed to obtain chemical information from measurement data. They also involve applying statistical methods such as machine learning algorithms. In these cases, a software is fed with training data sets for learning, which it uses as a measure for its analyses. By doing so, the software learns to make application-specific distinctions. This learning process is divided into two sections:

1. Analysis:
The software extracts all the required information from the spectra in a suitable form and in a short time. It does so by using principal component analysis (PCA) or the partial least squares (PLS) method.
2. Classification and modelling:
It then identifies the criteria used to distinguish the materials. These criteria are determined by using classification methods such as regression trees and models of multivariate regression such as Partial Least Squares regression (PLS) and principal component regression (PCR). These criteria are then used later on. Before you get a uniform view of the spectra, they must be normalised prior to examination to eliminate interference effects such as water bands or the shape of the white spectrum.

Principal component analysis (PCA)

Principal component analysis (PCA)

Our analysis software enables you to apply this method with all our instrument systems.

PCA starts off with reducing the number of variables used for analysis without losing important information. This is done to make detection as efficient as possible. The PCA approach is to find new coordinates along which the variance of the data set reaches its highest level. The projection coefficients on these coordinate axes are called scores and are later used for regression, i.e., classification. See the following PDF for an illustration of this process and the concepts behind it.

Partial least squares (PLS)

Partial least squares (PLS)

Our analysis software enables you to apply this method with all our instrument systems.

Our analysis software enables you to apply this method with all our instrument systems.
PLS starts off with reducing the number of variables used for analysis without losing important information. This is done to make detection as efficient as possible. The PLS approach is to find new coordinates along which the correlation (or covariance, in mathematical terms) between the data set and the categories reaches its highest level. The process is very similar to PCA but with a different form of constrained optimisation (see the PDF in the PCA section for additional illustration). The version of an algorithm with multiple categories is called PLSR2, but will also be referred to as PLS/PLSR in the following.

Classification - regression trees

Regression trees

Our analysis software enables you to apply this method with all our instrument systems.

Our analysis software enables you to apply this method with all our instrument systems.
The multi-stage regression trees method gradually refines the categorisation of materials. See the attached PDF for an example of a multi-stage regression tree. It starts with finding a node for rough subdivision (substrate or material), after which a PLSR is performed, which sorts the material in a range of predefined categories (types of metals). This process is repeated in each further node with other materials types until the complete classification is completed.

Modelling – linear regression (PLS regression, PCR)

PLS-regression, PCR

Our analysis software enables you to apply this method with all our instrument systems.

Principal Component Regression = PCR
Partial Least Squares Regression = PLSR2

These methods are analogous to multidimensional linear regression. However, the principal components of the respective analysis methods are used as coordinates. The process of linear regression is illustrated in the attached PDF file.


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