A validation is a check on the calibration function of new independent samples, in order to determine the error in the analysis method. As part of the cross-validation, the number of factors necessary for the calibration is determined. Cross- validation is achieved without new samples. For this purpose, the sample formulation which is intended for the calibration is subdivided into several groups. With a full cross-validation, as many groups are determined as there are samples, i.e. one sample per group. With larger data records, 3-5 groups are formed.
With a cross-validation with four groups, in pass 1 the samples of Group 1 are used for the validation, and only those of the remaining three groups are used for the actual calibration. In pass 2, Group 2 are used for the validation, in pass 3 Group 3, and so on. After the last pass, the statistical parameters of each individual pass of the cross-validation are determined, in order to establish at what number of factors the calibration exhibits the smallest error (SECV).
Cross-validation is necessary, because the risk of overfitting pertains, as can be seen from the Figure . With every additional wavelength or every additional factor the SEC falls, while the error in cross-validation (SECV) and the error of independent validation (SEP) rises again after the optimum number of wavelengths has been reached. With the aid of cross-validation the attempt is made to determine how many factors are necessary to obtain the smallest error in the NIRS analysis.
| Group1 | Group 2 | Group 3 | Group 4 |
| Sample 1 | Sample 2 | Sample 3 | Sample 4 |
| Sample 5 | Sample 6 | Sample 7 | Sample 8 |
| Sample 9 | Sample 10 | Sample 11 | Sample 12 |
| Sample 13 | Sample 14 | Sample 15 | Sample 16 |
| Sample 17 | Sample 18 | ... | ... |
Classification of the samples into four groups of a cross-validation
Error in calibration (SEC), cross-validation (SECV), and validation (SEP) with an increasing number of factors in the calibration equation (raw protein in horse beans)
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