Weighing schemes in multivariate data analysis

A collection of methods will be presented, designed to reflect special purpose or features in data. Many chemometric methods can be viewed as an application of special weighing schemes of the type presented here. After a short review of the H-principle of mathematical modelling, it will be applied to develop different weighing schemes and some simple ways to judge the quality or significance of a weighing scheme. Weighing schemes for two-way data will be established. We shall show how a loading vector can be adapted to a given score vector in order to improve the possibilities of interpretation of the results. These results will be extended to multiway data. It will be shown how we can develop different weighing schemes for multiway data depending on the purpose or interpretability of the results. The importance of these weighing schemes is due to the fact that they yield or emphasize the part of data that is 'in focus' in relation to the task in question. Copyright (C) 2001 John Wiley & Sons, Ltd.