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

Cite this: Anal. Chem. 2020, 92, 17, 11842–11850
Publication Date (Web):August 10, 2020
https://doi.org/10.1021/acs.analchem.0c02175
Copyright © 2020 American Chemical Society

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    Abstract

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    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.

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    • (Section S1) Computing the rotation matrix between two latent variable subspaces, (Figure S2) DoF and PRESS plots for the olives, and (Figure S3) PCA distance plots for A = 3 and 5 (PDF)

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