Conceptual aspects of multi-way data analysis

Multi-way Analysis With Applications in the Chemical Sciences. A. Smilde, R. Bro and R Geladi 2004 John Wiley Sons, Ltd ISBN 0-471-98691-7 

Multi-way Analysis With Applications in the Chemical Sciences 

Many of these aspects will be encountered in subsequent chapters and others are treated in 

Apart from these data analytical issues, the problem definition is important. Defining the problem is the core issue in all data analysis. It is not uncommon that data are analyzed by people not directly related to the problem at hand. If a clear understanding and consensus of the problem to be solved is not present, then the analysis may not even provide a solution to the real problem. Another issue is what kind of data are available or should be available Typical questions to be asked are is there a choice in instrumental measurements to be made and are some preferred over others are some variables irrelevant in the context, for example because they will not be available in the future can measurement precision be improved, etc. A third issue concerns the characteristics of the data to be used. Are they qualitative, quantitative, is the error distribution known within reasonable certainty, etc. The interpretation stage after data analysis usually refers back to the problem definition and should be done with the initial problem in mind. 

For a three-way array of liquid-chromatography-ultraviolet spectroscopy data, the samples are the objects whereas the absorbance at different retention times (of the chromatography mode) and the wavelengths (of the ultraviolet spectroscopy mode) are the two variable modes. Hence, absorbance is measured as a function of two properties retention time and wavelength. For a three-way array of food products x judges x sensory properties, the judge mode can be an object mode or a variable mode. In a preliminary analysis the judges 

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