3 Principal Component Analysis of Chemical Data

Publisher Summary The chapter presents a discussion on principal component analysis of chemical data. Chemistry demands for an exploratory data analysis frequently arise in connection with analytical work on complex samples, for example environmental samples and also in the field of structure-property-relationships. The discipline of chemometrics provides a number of methods to deal with such problems. During the past years, many of these methods became available for personal computers (PCs), either by statistical software packages or by specific software developed by chemists. A variety of chemometric methods is, in principle, now available at the chemist's own desk. The chemist is forced to use such methods, because of the complexity of actual problems in chemistry. The chapter presents an introduction and outlines some fundamentals of interpretation and processing of multivariate data. The chapter focuses on a user-oriented description of basic aspects of principal component analysis (PCA). PCA is an excellent tool for exploratory data analysis in chemistry. The chapter discusses the multivariate chemical data. Cluster analysis investigates the existence of natural groups (clusters) of objects. When clusters can be found, similarities between the members of a cluster have to be established. The most important method for exploratory analysis of multivariate data is reduction of the dimensionality and graphical representation of the data. The method that is essentially a rotation of the coordinate system is also referred to as “eigenvector-projection” or “Karhunen-Loeve- projection.” An example from the field of environmental analytical chemistry is chosen to demonstrate the application of PCA. The data is taken from an investigation on air pollution in the city of Vienna (Austria) by polycyclic aromatic hydrocarbons (PAH).