Review on Multiway Analysis in Chemistry—2000-2005

INTRODUCTION

Multiway analysis is concerned with the analysis of higher order data as defined, e.g., by Henk Kiers (1). Higher-order data is data that can be arranged in boxes as opposed to two-way data, matrices, that can be arranged in tables. Interestingly, the paper by Kiers, describes the first suggestion for a standardized notation for multiway analysis not only applicable in chemistry, but in data analysis in general. It is advised to use these suggestions for notation in order to make communication across and within different disciplines more straightforward.

Multiway data occurs frequently due to modern instrumental developments, so it is quite typical that multiway data analysis in recent years has been applied to new advanced instrumental data. But the maturing of the area has also led to a situation where multiway tools are more frequently used for other types of data such as process data, sensory data, etc. In certain situations, multiway data are rearranged into matrices and analyzed using ordinary multivariate data analysis, two-way analysis. This review does not go into such extensions of two-way analysis, but focuses on the tools that work directly on the three-way data or in general multiway data. Multiway analysis started in psychometrics in the 1960s and 1970s (2, 3, 4, 5) partly based on problems in factor analysis dating back to the 1940s (6). Since then there has been an increasing collaboration between psychometricians and chemometricians on both fundamental and applied issues. In later years, multiway analysis has started to be used in signal processing and mathematics, but most results from these areas will not be covered in this review as they are of little relevance to chemical applications.

As an indication of the growth in multiway analysis, the period that this a review deals with has also witnessed a whole special issue of the Journal of Chemometrics devoted to multiway analysis (7) as well as the first book on multiway analysis (8) in chemistry. A review covering the 10-year period 1985 to 1995 contained 126 references (9) whereas this 5-year review contains more than 300 papers.

In the following the literature on multiway analysis is described in terms of three different types of areas. The first part of the review describes applications in terms types of data, while the second part describes multiway analysis in terms of different areas of application, and finally more theoretical aspects of multiway analysis are described.