Ph. D. Thesis 2. Theory – Fundamentals of the Multivariate Data Analysis 2.4. Data Splitting and Validation 2.4.1. Crossvalidation
 Home News About Me Ph. D. Thesis Abstract Table of Contents 1. Introduction 2. Theory – Fundamentals of the Multivariate Data Analysis 2.1. Overview of the Multivariate Quantitative Data Analysis 2.2. Experimental Design 2.3. Data Preprocessing 2.4. Data Splitting and Validation 2.4.1. Crossvalidation 2.4.2. Bootstrapping 2.4.3. Random Subsampling 2.4.4. Kennard Stones 2.4.5. Kohonen Neural Networks 2.4.6. Conclusions 2.5. Calibration of Linear Relationships 2.6. Calibration of Nonlinear Relationships 2.7. Neural Networks – Universal Calibration Tools 2.8. Too Much Information Deteriorates Calibration 2.9. Measures of Error and Validation 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 11. Summary and Outlook 12. References 13. Acknowledgements Publications Research Tutorials Downloads and Links Contact Search Site Map Print this Page

2.4.1.   Crossvalidation

The most popular subsampling technique is crossvalidation. For an n-fold crossvalidation, the data are partitioned into n equal parts. The first part is used as test data set; the rest is used as calibration data set. Then, the second part is used for the test data and the rest is used for a new calibration. This procedure is repeated n times and the predictions of the n test data are averaged. It is essential that no knowledge of the models is transferred from fold to fold. There exist no clear rules how many folds to use for the crossvalidation, whereby the simplest and clearest way of performing crossvalidation is to leave one sample out at a time. This special variant of crossvalidation is also called full crossvalidation, leave-one-out or jackknifing and gives a unique and therefore reproducible result. Yet, it has been shown that increasing the number of crossvalidation groups results in lower root mean square errors of predictions giving overly optimistic estimations of predictivity [13]-[16]. This deficiency is known as asymptotically inconsistency in literature [17].

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