Can One Recover the Underlying Spectral Data Matrix From a Given Borgen Plot?

IF 2.3 4区化学 Q1 SOCIAL WORK

Journal of Chemometrics Pub Date : 2025-03-08 DOI:10.1002/cem.70016

Martina Beese, Tomass Andersons, Mathias Sawall, Hamid Abdollahi, Klaus Neymeyr

{"title":"Can One Recover the Underlying Spectral Data Matrix From a Given Borgen Plot?","authors":"Martina Beese, Tomass Andersons, Mathias Sawall, Hamid Abdollahi, Klaus Neymeyr","doi":"10.1002/cem.70016","DOIUrl":null,"url":null,"abstract":"In multivariate curve resolution (MCR), Borgen plots represent the regions of feasible pure component profiles underlying spectral mixture data. A Borgen plot can be constructed geometrically in the low-dimensional <math>\n <semantics>\n <mrow>\n <mi>U</mi>\n </mrow>\n <annotation>$$ U $$</annotation>\n </semantics></math>- and <math>\n <semantics>\n <mrow>\n <mi>V</mi>\n </mrow>\n <annotation>$$ V $$</annotation>\n </semantics></math>-spaces if the so-called outer polygon (representing nonnegativity constraints) and the inner polygon (i.e., the convex hull of the data representing points) are given. This paper asks whether it is possible to construct spectral data from the data representing points spanning the polygons and thus reconstruct the data from the associated Borgen plot. A partially positive answer is given.","PeriodicalId":15274,"journal":{"name":"Journal of Chemometrics","volume":"39 3","pages":""},"PeriodicalIF":2.3000,"publicationDate":"2025-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1002/cem.70016","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Chemometrics","FirstCategoryId":"92","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1002/cem.70016","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

In multivariate curve resolution (MCR), Borgen plots represent the regions of feasible pure component profiles underlying spectral mixture data. A Borgen plot can be constructed geometrically in the low-dimensional $U$ - and $V$ -spaces if the so-called outer polygon (representing nonnegativity constraints) and the inner polygon (i.e., the convex hull of the data representing points) are given. This paper asks whether it is possible to construct spectral data from the data representing points spanning the polygons and thus reconstruct the data from the associated Borgen plot. A partially positive answer is given.

Abstract Image

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Journal of Chemometrics 化学-分析化学

CiteScore

5.20

自引率

8.30%

发文量

审稿时长

2 months

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.