Principal component analysis and PARAFAC

A short introduction to principal component analysis for two-way arrays and PARAFAC for three-way arrays will be given here. These methods are used in the next chapter, and therefore, a short introduction is necessary. Definitions, notations and other details on these methods are explained in later chapters. 

A pair of a loading vector and a matching score vector is called a component for PCA and similarly, a triplet of loading vectors is called a PARAFAC component. The distinction between a loading and a score vector is relatively arbitrary. Usually, the term score vector is 

Multi-way Analysis With Applications in the Chemical Sciences 

This chapter introduces multi-way analysis and describes important concepts of data analysis in general. In data analysis, sometimes a distinction is made between objects and variables. Such distinctions are not always clear. Moreover, there is a large variety of types of variables, such as homogenous or heterogenous. It is important to keep these things in mind when doing multi-way analysis. 

An overview is given of the different kinds of possible multi-way analyses and existing methods to perform such analyses. A categorization is presented in which different multi-way analyses are divided into classes using two criteria (i) the number of blocks involved, and (ii) the order of the arrays involved. Practical examples are given for each class, showing the relevance of the multi-way analysis problem. 

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