Title: principal-component analysis
Long Title: IUPAC Gold Book - principal-component analysis
DOI: 10.1351/goldbook.10106
Status: current

Definition
Factor analysis in which factors are calculated that successively capture the greatest variance in the data set.

Notes
1) The factors are orthogonal and are known as principal-component factors.
2) The factorization is written \(\boldsymbol{X} = \boldsymbol{T}\boldsymbol{P}^{\rm{T}} + \boldsymbol{E}\), where \(\boldsymbol{T}\) is the scores matrix, \(\boldsymbol{P}\) is the loadings matrix and \(\boldsymbol{E}\) is a residual matrix.
3) The term "principal-component analysis" is preferred to the plural "principal-components analysis".

Related Terms
- Factor analysis: https://goldbook.iupac.org//terms/view/10093
- loadings: https://goldbook.iupac.org//terms/view/10096
- non-linear iterative partial least squares: https://goldbook.iupac.org//terms/view/10101
- principal-component factors: https://goldbook.iupac.org//terms/view/10107
- scores: https://goldbook.iupac.org//terms/view/10112

Source
- PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 423 (https://doi.org/10.1515/pac-2015-0605)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10106/html
- json: https://goldbook.iupac.org/terms/view/10106/json
- xml: https://goldbook.iupac.org/terms/view/10106/xml

Citation: Citation: 'principal-component analysis' 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.10106
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Accessed: 2026-04-18T20:44:09+00:00