{"term":{"id":"10053","title":"mean centering","longtitle":"IUPAC Gold Book - mean centering","doi":"10.1351\/goldbook.10053","code":"10053","status":"current","synonym":"<em>synonym<\/em>: centering","definitions":[{"id":1,"text":"Data pre-processing in which the mean value of a variable is subtracted from data across all objects. \\[a_{i,j}^{\\ast} = a_{i,j} - \\frac{1}{n} \\sum \\limits_{i\\,=\\,1}^{n} a_{i,j}\\]","notes":{"1":"Mean centering emphasises the differences between samples rather than differences between the samples and the variable’s origin (zero).","2":"Mean centering is generally recommended for principal component analysis, partial least squares and discriminant analysis of data, where relative values across the samples are more important than their absolute deviation from zero. Mean centering is not compatible with non-negativity constraints in, for example, multivariate curve resolution.","3":"Mean centering is generally applied with other data pre-processing methods."},"links":[{"term":"Scaling","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10060"},{"term":"data pre-processing","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10048"},{"term":"multivariate curve resolution","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10100"},{"term":"partial least squares","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10155"},{"term":"principal component analysis","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10106"}],"sources":["PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 410 (https:\/\/doi.org\/10.1515\/pac-2015-0605)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/10053\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/10053\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/10053\/plain"},"citation":"Citation: 'mean centering' 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.10053","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":"2026-05-30T17:25:28+00:00"}}