Pattern recognition factor analysis principal components

Nowadays, generating huge amounts of data is relatively simple. That means Data Reduction and Interpretation using multivariate statistical tools (chemometrics), such as pattern recognition, factor analysis, and principal components analysis, can be critically important to extracting useful information from the data. These subjects have been introduced in Chapters 5 and 6. 

The answers to these questions will usually be given by so-called unsupervised learning or unsupervised pattern recognition methods. These methods may also be called grouping methods or automatic classification methods because they search for classes of similar objects (see cluster analysis) or classes of similar features (see correlation analysis, principal components analysis, factor analysis). 

CONTENTS 1. Chemometrics and the Analytical Process. 2. Precision and Accuracy. 3. Evaluation of Precision and Accuracy. Comparison of Two Procedures. 4. Evaluation of Sources of Variation in Data. Analysis of Variance. 5. Calibration. 6. Reliability and Drift. 7. Sensitivity and Limit of Detection. 8. Selectivity and Specificity. 9. Information. 10. Costs. 11. The Time Constant. 12. Signals and Data. 13. Regression Methods. 14. Correlation Methods. 15. Signal Processing. 16. Response Surfaces and Models. 17. Exploration of Response Surfaces. 18. Optimization of Analytical Chemical Methods. 19. Optimization of Chromatographic Methods. 20. The Multivariate Approach. 21. Principal Components and Factor Analysis. 22. Clustering Techniques. 23. Supervised Pattern Recognition. 24. Decisions in the Analytical Laboratory. 

Among the multivariate methods the most important are principal components analysis (PCA), factor analysis, cluster analysis and the pattern recognition method, from which only PCA will be briefly described below. PCA is used to find such a system of new variables, called principal components (PC), which explains the variation of a given data set in a more convenient way than the original system of variables, e.g. xl9...,Xj,...,xm. The greater convenience of PC consists mainly in a reduction of dimensions, m, in which the data were originally described, because the PC variables are chosen so that only two or three of them should be sufficient to characterize the variation of the data. The PC are linear combinations of the original variables, xj9 used to characterize the set of objects,... 

To find patterns in data and to assign samples, materials, or, in general, objects, to those patterns, multivariate methods of data analysis are applied. Recognition of patterns, classes, or clusters is feasible with projection methods, such as principal component analysis or factor analysis, or with cluster analysis. To construct class models for classification of unknown objects, we will introduce discriminant analyses. 

One possibility to speedup the search is preliminary sorting of the data sets. Here, the methods of unsupervised pattern recognition are used, for example, principal component and factor analysis, cluster analysis, or neural networks (cf. Sections 5.2 and 8.2). The unknown spectrum is then compared with every class separately. 

When FT-NIR data is combined with chemometrics, the increase in the amount of information available from the spectra are substantially increased, including the ability to separate very similar materials and to differentiate between materials of various grades and qualities. Chemometrics provides the algorithms for software to perform pattern recognition on the spectra. The most discerning method. Cluster Analysis, is based on software that uses factor analysis or principal components. This method is more objective as circles of tolerance are built with about five lots of typical material that has been tested according to reference methods. 

Frequently the efforts are hampered by the lack of a sufficiently large number of samples. In our experience, it appears to be helpful if the number of samples exceeds the number of parameters (wavenumber intervals, principal components, latent variables, etc.) by at least a factor of five. This finding is supported by calculating this ratio between the number of teaching samples and the number of parameters both in the field of diagnostic pattern recognition (see the column ratio in Table 6.2) as well as in the quantitative analysis of serum. 

There are now several curve-fitting methods available on most AES/XPS systems. Among these may be mentioned principal component analysis (factor analysis), linear least-squares fitting, the maximum entropy method, the pattern recognition method (derived from factor analysis) and difference spectra. 

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