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Ph. D. ThesisPh. D. Thesis 10. Results  Various Aspects of the Frameworks and Measurements10. Results Various Aspects of the Frameworks and Measurements 10.1. Single or Multiple Analyte Rankings10.1. Single or Multiple Analyte Rankings
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Ph. D. Thesis
  Abstract
  Table of Contents
  1. Introduction
  2. Theory Fundamentals of the Multivariate Data Analysis
  3. Theory Quantification of the Refrigerants R22 and R134a: Part I
  4. Experiments, Setups and Data Sets
  5. Results Kinetic Measurements
  6. Results Multivariate Calibrations
  7. Results Genetic Algorithm Framework
  8. Results Growing Neural Network Framework
  9. Results All Data Sets
  10. Results Various Aspects of the Frameworks and Measurements
    10.1. Single or Multiple Analyte Rankings
    10.2. Stopping Criteria for the Parallel Frameworks
    10.3. Optimization of the Measurements
    10.4. Robustness and Comparison with Martens' Uncertainty Test
  11. Summary and Outlook
  12. References
  13. Acknowledgements
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10.1.   Single or Multiple Analyte Rankings

In principle, the variable selection of the frameworks can be performed for each analyte (response variable) separately or for all analytes together. For example, the variable selection by the parallel growing neural network was performed for each analyte separately in section 8.4.1 by using a separate ranking for both analytes, whereas the variable selection in the sections 9.1.2, 9.2.4, 9.3.2 and 9.3.3 was performed for all analytes together by using a combined ranking for all analytes together (addition of the individual rankings). In the second step of the iterative variable addition procedure, the combined ranking saves about n times the computing time for n analytes. Yet the question is, if a separate variable selection performs significantly better.

Thus, the ternary mixtures of methanol, ethanol and 1-propanol measured by SPR and evaluated by the parallel growing network framework (see section 9.2.4) were evaluated again using a separate ranking for each analyte and separate iterative addition steps (step 2 of the framework). The RMSE of the validation data, which are shown in table 10, are very similar and do not allow a clear decision which method to prefer.

Variable Selection

Meth.

Eth.

Prop.

Together

3.31

6.05

7.33

Separate

3.30

6.15

7.25

table 10: Relative RMSE in % for the prediction of the validation data measured by SPR and evaluated by the parallel growing neural network framework.

Evaluating the parallel growing network framework of the refrigerant data together instead of separately (compare with 4th row of table 4 in chapter 8) resulted in slightly worse predictions of 2.08% for the validation data of R22 instead of 2.04% and slightly better predictions for R134a with 2.53% instead of 2.61%. For other data sets, also no clear preference can be seen rendering the more computing intensive separate variable selection superfluous.

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