Multi-way Analysis in the Food Industry

This thesis describes some of the recent developments in multi-way analysis in the field of chemometrics. Originally, the primary purpose of this work was to test the adequacy of multi-way models in areas related to the food industry. However, during the course of this work, it became obvious that basic research is still called for. Hence, a fair part of the thesis describes methodological developments related to multi-way analysis. A multi-way calibration model inspired by partial least squares regression is described and applied (N-PLS). Different methods for speeding up algorithms for constrained and unconstrained multi-way models are developed (compression, fast non-negativity constrained least squares regression). Several new constrained least squares regression methods of practical importance are developed (unimodality constrained regression, smoothness constrained regression, the concept of approximate constrained regression). Several models developed in psychometrics that have never been applied to real-world problems are shown to be suitable in different chemical settings. The PARAFAC2 model is suitable for modeling data with factors that shift. This is relevant, for example, for handling retention time shifts in chromatography. The PARATUCK2 model is shown to be a suitable model for many types of data subject to rank-deficiency. A multiplicative model for experimentally designed data is presented which extends the work of Mandel, Gollob, and Hegemann for two-factor experiments to an arbitrary number of factors. A matrix product is introduced which for instance makes it possible to express higher-order PARAFAC models using matrix notation. Implementations of most algorithms discussed are available in MATLAB code at http://newton.foodsci.kvl.dk. To further facilitate the