{"term":{"id":"10111","title":"simple-to-use interactive self-modelling mixture analysis","longtitle":"IUPAC Gold Book - simple-to-use interactive self-modelling mixture analysis","doi":"10.1351\/goldbook.10111","code":"10111","status":"current","initialism":"<em>initialism<\/em>: SIMPLISMA","definitions":[{"id":1,"text":"Interactive method to obtain concentrations and pure spectra from spectra of mixtures using directly-measured variables.","notes":{"1":"The directly-measured variables are called \"pure variables\" in the method.","2":"A data matrix \\(\\boldsymbol{D} = \\boldsymbol{C} \\times \\boldsymbol{P}^{\\rm{T}} + \\boldsymbol{E}\\) where \\(\\boldsymbol{C}\\) is a concentration matrix, \\(\\boldsymbol{P}\\) pure spectra of mixture components and \\(\\boldsymbol{E}\\) an error matrix. Pure spectra are estimated \\(\\boldsymbol{\\hat Y}\\) which allows projection of a concentration matrix \\(\\boldsymbol{C^{\\ast}}\\) from which the data matrix can be reconstructed and compared with the measured spectra. \\[\\left\\{ {\\matrix{ {\\boldsymbol{\\hat P} = \\boldsymbol{D}^{\\rm{T}} \\boldsymbol{C}(\\boldsymbol{C}^{\\rm{T}}\\boldsymbol{C})}^{-1} \\cr {\\boldsymbol{C^{*}} = \\boldsymbol{C}\\boldsymbol{\\hat P}(\\boldsymbol{\\hat P}^{\\rm{T}}\\boldsymbol{\\hat P})}^{-1} \\cr}} \\right. {\\rm{then}}\\;{\\boldsymbol{D}_{{\\rm{recon}}}} = \\boldsymbol{C^{*}} \\times \\boldsymbol{\\hat P}^{\\rm{T}}\\]","3":"Second derivatives of spectra can be used for modelling."},"links":[{"term":"data matrix","url":"https:\/\/goldbook.iupac.org\/\/terms\/view\/10047"}],"sources":["PAC, 2016, 88, 407. 'Vocabulary of concepts and terms in chemometrics (IUPAC Recommendations 2016)' on page 424 (https:\/\/doi.org\/10.1515\/pac-2015-0605)"]}],"altoutputs":{"html":"https:\/\/goldbook.iupac.org\/terms\/view\/10111\/html","xml":"https:\/\/goldbook.iupac.org\/terms\/view\/10111\/xml","plain":"https:\/\/goldbook.iupac.org\/terms\/view\/10111\/plain"},"citation":"Citation: 'simple-to-use interactive self-modelling mixture 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.10111","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":"2026-04-20T09:29:55+00:00"}}