alternating least squares regression

synonym: alternating regression
initialism: ALS
https://doi.org/10.1351/goldbook.10083

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.

Note: 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.
Source:
PAC, 2016, 88, 407. (Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)) on page 417 [Terms] [Paper]
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. https://doi.org/10.1351/goldbook.10083 RIS BibTex EndNote
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