Procrustes Cross-Validation-A Bridge between Cross-Validation and Independent Validation Sets

In this paper, we propose a new approach for validation of chemometric models. It is based on k-fold cross-validation algorithm, but in contrast to conventional cross-validation, our approach makes it possible to create a new dataset, which carries sampling uncertainty estimated by the cross-validation procedure. This dataset, called a pseudo-validation set, can be used similar to an independent test set, giving a possibility to compute residual distances, explained variance, scores, and other results, which cannot be obtained in the conventional cross-validation. The paper describes theoretical details of the proposed approach and its implementation as well as presents experimental results obtained using simulated and real chemical datasets.