{"title":"Adjusted Pareto Scaling for Multivariate Calibration Models","authors":"Kurt Varmuza, Peter Filzmoser","doi":"10.1002/cem.3588","DOIUrl":null,"url":null,"abstract":"The performance of multivariate calibration models <jats:italic>ŷ</jats:italic> = f(<jats:italic>x</jats:italic>) for the prediction of a numerical property <jats:italic>y</jats:italic> from a set of <jats:italic>x</jats:italic>‐variables depends on the type of scaling of the <jats:italic>x</jats:italic>‐variables. Common scaling methods are autoscaling (dividing the centered <jats:italic>x</jats:italic> by its standard deviation <jats:italic>s</jats:italic>) and Pareto scaling (dividing the centered <jats:italic>x</jats:italic> by <jats:italic>s</jats:italic><jats:sup><jats:italic>P</jats:italic></jats:sup> with <jats:italic>p</jats:italic> = 0.5). The adjusted Pareto scaling presented here varies the exponent <jats:italic>P</jats:italic> between 0 (no scaling) and 1 (autoscaling) with the aim of obtaining an optimum prediction performance for <jats:italic>ŷ</jats:italic>. Related scaling methods based on the variable spread are range scaling and vast scaling; while level scaling is based on the location (central value) of the variable. These scaling methods and robust versions are compared for models created by partial least‐squares (PLS) regression. The applied strategy repeated double cross validation (rdCV) evaluates the model performance for test set objects and considers its variability. Results with three data sets from chemistry show: (a) the efficacy of the different scaling methods depends on the data structure; (b) optimization of the Pareto exponent <jats:italic>P</jats:italic> is recommended; (c) range scaling or vast scaling may be better than adjusted Pareto scaling; (d) in general a heuristic search for the best scaling method is advisable. Overall, the consideration of different variants of scaling allow for a flexible adjustment of the variable contributions to the calibration model.","PeriodicalId":15274,"journal":{"name":"Journal of Chemometrics","volume":null,"pages":null},"PeriodicalIF":2.3000,"publicationDate":"2024-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Chemometrics","FirstCategoryId":"92","ListUrlMain":"https://doi.org/10.1002/cem.3588","RegionNum":4,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"SOCIAL WORK","Score":null,"Total":0}
引用次数: 0
Abstract
The performance of multivariate calibration models ŷ = f(x) for the prediction of a numerical property y from a set of x‐variables depends on the type of scaling of the x‐variables. Common scaling methods are autoscaling (dividing the centered x by its standard deviation s) and Pareto scaling (dividing the centered x by sP with p = 0.5). The adjusted Pareto scaling presented here varies the exponent P between 0 (no scaling) and 1 (autoscaling) with the aim of obtaining an optimum prediction performance for ŷ. Related scaling methods based on the variable spread are range scaling and vast scaling; while level scaling is based on the location (central value) of the variable. These scaling methods and robust versions are compared for models created by partial least‐squares (PLS) regression. The applied strategy repeated double cross validation (rdCV) evaluates the model performance for test set objects and considers its variability. Results with three data sets from chemistry show: (a) the efficacy of the different scaling methods depends on the data structure; (b) optimization of the Pareto exponent P is recommended; (c) range scaling or vast scaling may be better than adjusted Pareto scaling; (d) in general a heuristic search for the best scaling method is advisable. Overall, the consideration of different variants of scaling allow for a flexible adjustment of the variable contributions to the calibration model.
期刊介绍:
The Journal of Chemometrics is devoted to the rapid publication of original scientific papers, reviews and short communications on fundamental and applied aspects of chemometrics. It also provides a forum for the exchange of information on meetings and other news relevant to the growing community of scientists who are interested in chemometrics and its applications. Short, critical review papers are a particularly important feature of the journal, in view of the multidisciplinary readership at which it is aimed.