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Bi‐modal OnPLS
Author(s) -
Löfstedt Tommy,
Eriksson Lennart,
Wormbs Gunilla,
Trygg Johan
Publication year - 2012
Publication title -
journal of chemometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.47
H-Index - 92
eISSN - 1099-128X
pISSN - 0886-9383
DOI - 10.1002/cem.2448
Subject(s) - row , row and column spaces , extension (predicate logic) , modal , variation (astronomy) , covariance matrix , set (abstract data type) , matrix (chemical analysis) , mathematics , column (typography) , space (punctuation) , block (permutation group theory) , algorithm , interpretation (philosophy) , data set , computer science , statistics , combinatorics , geometry , chromatography , materials science , chemistry , physics , database , connection (principal bundle) , astrophysics , polymer chemistry , programming language , operating system
This paper presents an extension to the recently published OnPLS data analysis method. Bi‐modal OnPLS allows for arbitrary block relationships in both columns and rows and is able to extract orthogonal variation in both columns and rows without bias towards any particular direction or matrix: the method is fully symmetric with regard to both rows and columns. Bi‐modal OnPLS extracts a minimal number of globally predictive score vectors that exhibit maximal covariance and correlation in the column space and a corresponding set of predictive loading vectors that exhibit maximal correlation in the row space. The method also extracts orthogonal variation (i.e. variation that is not related to all other matrices) in both columns and rows. The method was applied to two synthetic datasets and one real data set regarding sensory information and consumer likings of dairy products. It was shown that Bi‐modal OnPLS greatly improves the intercorrelations between both loadings and scores while still finding the correct variation. This facilitates interpretation of the predictive components and makes it possible to study the orthogonal variation in the data. Copyright © 2012 John Wiley & Sons, Ltd.