AuthorsG. Tomasi, E. A. Ataman and R. Bro
EditorsS. Brown, R. Tauler and B. Walczak
TitleMultilinear Models, Iterative Methods
AfilliationMachine Learning
Project(s)Department of Data Science and Knowledge Discovery
Publication TypeBook Chapter
Year of Publication2020
Book TitleComprehensive Chemometrics (Second Edition)
Secondary TitleChemical and Biochemical Data Analysis
ISBN Number978-0-12-409547-2
Keywords-way Tucker models, CANDECOMP, Curve resolution, Exploratory analysis, Least squares, Linked mode PARAFAC, Multi-way analysis, Multi-way array, Multilinear model, PARAFAC, PARAFAC2, PARALIND, Restricted Tucker models, Tensor decomposition, Tensor-matrix factorization

In this section, multilinear models for multi-way arrays requiring iterative fitting algorithms are outlined. Among them: the PARAFAC (PARAllel FACtor analysis) model and one of its variants (the PARAFAC2 model); Tucker models in which one or more modes are reduced (viz., the N-way Tucker-N and Tucker-m models); hybrid models having intermediate properties between PARAFAC and Tucker ones; and coupled matrix and tensor decompositions (CMTF) which simultaneously decomposes multiple tensors. Five examples are included as to illustrate some practical aspects concerning the use of these models on analytical data.