ABSTRACT
Chromatographic experiments often derive a multivariate dataset, which can be presented and analyzed as a matrix. Multivariate datasets are obtained for objects (e.g., samples) having some properties (e.g., peak areas), and for each object all properties are measured. The analysis of multivariate data is based on a geometrical assumption, that the objects can be seen as points in a multivariate space with the dimensionality equal to the number of properties. The multivariate treatment allows defining many measures of similarity (or dissimilarity) between objects. The factorization of a matrix is its decomposition into a product of several matrices. In multivariate data analysis, chemometricians seek for specially positioned subspaces to maximize the compressed information and to minimize the lost information. This can only be done if the data is compressible, and the most popular approach for defining such subspaces is principal component analysis.
