10083 IUPAC Gold Book - alternating least squares regression 10.1351/goldbook.10083 10083 current initialism: ALS synonym: alternating regression 1 Solution to the multivariate decomposition of a data matrix in which iteratively a solution of one output matrix is used to compute the second matrix, after the application of constraints. ALS is used to decompose multiple spectra (\(\boldsymbol{X}\)) into concentration (\(\boldsymbol{C}\)) and component spectra (\(\boldsymbol{S}\)). \(\boldsymbol{X} = \boldsymbol{C}\boldsymbol{S}^{\rm{T}}\). Because spectra and concentrations cannot be negative at each iteration negative values are set to zero. multivariate https://goldbook.iupac.org//terms/view/10055 PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 417 (https://doi.org/10.1515/pac-2015-0605) https://goldbook.iupac.org/terms/view/10083/html https://goldbook.iupac.org/terms/view/10083/json https://goldbook.iupac.org/terms/view/10083/plain Citation: 'alternating least squares regression' 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.10083 The IUPAC Gold Book is licensed under Creative Commons Attribution-ShareAlike CC BY-SA 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) for individual terms. If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org . The International Union of Pure and Applied Chemistry (IUPAC) is continuously reviewing and, where needed, updating terms in the Compendium of Chemical Terminology (the IUPAC Gold Book). Users of these terms are encouraged to include the version of a term with its use and to check regularly for updates to term definitions that you are using. 2026-04-18T12:45:13+00:00