Title: nonlinear mapping
Long Title: IUPAC Gold Book - nonlinear mapping
DOI: 10.1351/goldbook.10102
Status: current

Definition
Projection of objects defined in a multivariate space onto two- or three-dimensional space so that the distances between objects are preserved as well as possible.

Notes
1) An often applied criterion for the mapping error (\(E\)) is the relative squared error between the true distance \(d_{ij}\) and mapped distance \(\delta_{ij}\).
2) Several iterative optimization procedures can be applied to minimize \(E\), such as steepest descent.

Source
- PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 422 (https://doi.org/10.1515/pac-2015-0605)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10102/html
- json: https://goldbook.iupac.org/terms/view/10102/json
- xml: https://goldbook.iupac.org/terms/view/10102/xml

Citation: Citation: 'nonlinear mapping' in IUPAC Compendium of Chemical Terminology, 5th ed. International Union of Pure and Applied Chemistry; 2025. Online version 5.0.0, 2025. 10.1351/goldbook.10102
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Accessed: 2026-08-06T06:44:43+00:00