A similarity index for comparing coupled matrices. (19th June 2018)

• Record Type: Journal Article
• Authors: Indahl, Ulf G.; Næs, Tormod; Liland, Kristian Hovde
• Is Part Of: Journal of chemometrics. Volume 32:Number 10(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-06-19
• Subjects: canonical correlation -- orthogonal projections -- Procrustes rotations -- RV coefficient -- significance testing -- similarity index; Chemistry -- Mathematics -- Periodicals; Chemistry -- Statistical methods -- Periodicals; 542.85
• DOI: 10.1002/cem.3049
• Languages: English
• ISSNs: 0886-9383

Abstract

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. Abstract : Application of different multivariate measurement technologies to the same set of samples is an interesting challenge in many modern fields of applied data analysis. We propose a 2‐stage similarity index framework for comparing 2 matrices in this type of situation. Our approach is based on identifying factors (and associated subspaces), followed by the assignment of statistical significances to the similarity values associated with the various factor subset combinations.