Multi-Way Analysis

Multi--way analysis is an increasingly important method of data analysis which can be used in a large number of fields in chemistry and other disciplines. This book is an introduction to the field of multi--way analysis for chemists and chemometricians, focusing on the ideas behind the method and its practical applications. This book presents a detailed description of three-way and multi-way arrays, their properties and the methods utilised to model these arrays mathematically. Multi-way component analysis is introduced by its two most important models - Tucker3 and PARAFAC. In addition, intermediate and derived models are included. Multi-way regression methods receive special attention and a number of algorithms are presented. The book includes detailed accounts of diagnostics, visualization of results and handling of residuals. Appropriate attention is given to the preprocessing of data. Mathematical rigor is applied where necessary and numerous proofs are included. The book concludes with an overview of the different application fields of multi-way analysis, including analytical chemistry, process monitoring, environmental analysis and three-way data resulting from ANOVA or designed experiments. The relationship of these methods to chemistry is always emphasized. The book is aimed at researchers who are interested in theoretical and practical aspects of data analysis. It is directly relevant to chemical sciences such as analytical, environmental, clinical and physical chemistry. In addition, it is pertinent to chemometrics, bioinformatics, biochemistry, process analysis, food chemistry and sensory analysis.