ABSTRACT
A multivariate dataset, arranged as a matrix, can be interpreted as an example of two-way dataset. A two-way dataset is the simplest example of a multiway dataset. PARAFAC is a basic method of decomposition of a three-way (or multiway) array to several sets of "scores. One of the main advantages of PARAFAC is that the solution is unique and there is no rotational freedom as with principal components analysis (PCA). Tucker3 differs from PARAFAC by the presence of an additional tensor green with weights, which is a cube with dimensions equal to decomposition factors. It incorporates additional degrees of freedom, as the final tensor is a weighted sum of score vectors. The classical approaches for building a model to predict a sample property from a chromatogram are based on multivariate regression methods. However, when using multiresponse detectors, a chromatogram becomes a matrix—it is a two-way dataset, having time as the one factor/dimension and detection property along the second dimension.
