Volume 32, Issue 10 e3049
RESEARCH ARTICLE

A similarity index for comparing coupled matrices

Ulf G. Indahl

Corresponding Author

Ulf G. Indahl

Faculty of Sciences and Technology, Norwegian University of Life Sciences, N-1432 Ås, Norway

Correspondence

Ulf G. Indahl, Faculty of Sciences and Technology, Norwegian University of Life Sciences, N-1432 Ås, Norway.

Email: [email protected]

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Tormod Næs

Tormod Næs

Nofima, 1430 Ås, Norway

Dept. of Food Science, University of Copenhagen, Copenhagen, Denmark

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Kristian Hovde Liland

Kristian Hovde Liland

Faculty of Sciences and Technology, Norwegian University of Life Sciences, N-1432 Ås, Norway

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First published: 19 June 2018
Citations: 26

Abstract

Application of different multivariate measurement technologies to the same set of samples is an interesting challenge in many fields of applied data analysis. Our proposal is a 2-stage similarity index framework for comparing 2 matrices in this type of situation. The first step is to identify factors (and associated subspaces) of the matrices by methods such as principal component analysis or partial least squares regression to provide good (low-dimensional) summaries of their information content. Thereafter, statistical significances are assigned to the similarity values obtained at various factor subset combinations by considering orthogonal projections or Procrustes rotations and how to express the results compactly in corresponding summary plots. Applications of the methodology include the investigation of redundancy in spectroscopic data and the investigation of assessor consistency or deviations in sensory science. The proposed methodology is implemented in the R-package “MatrixCorrelation” available online from CRAN.