Title: variance scaling
Long Title: IUPAC Gold Book - variance scaling
DOI: 10.1351/goldbook.10064
Status: current

Definition
Scaling in which the scaling matrix is the standard deviation of each variable across the objects. \[a_{i,j}^{\ast} = \frac{a_{i,j}}{s_{j}}\]

Notes
1) A variable occupies a column of the data matrix.
2) Variance scaling equalizes the importance of each variable in multivariate data.
3) When used with mean centering variance scaling is known as autoscaling.

Related Terms
- Scaling: https://goldbook.iupac.org//terms/view/10060
- autoscaling: https://goldbook.iupac.org//terms/view/10044
- data matrix: https://goldbook.iupac.org//terms/view/10047
- mean centering: https://goldbook.iupac.org//terms/view/10053
- multivariate data: https://goldbook.iupac.org//terms/view/10055

Source
- PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 413 (https://doi.org/10.1515/pac-2015-0605)

Other Outputs
- html: https://goldbook.iupac.org/terms/view/10064/html
- json: https://goldbook.iupac.org/terms/view/10064/json
- xml: https://goldbook.iupac.org/terms/view/10064/xml

Citation: Citation: 'variance scaling' 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.10064
License: 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.
Collection: If you are interested in licensing the Gold Book for commercial use, please contact the IUPAC Executive Director at executivedirector@iupac.org .
Disclaimer: 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.
Accessed: 2026-04-18T20:51:31+00:00