ABSTRACT
This chapter treats the foundations of OODA. An important aspect is terminology that is designed to make the main ideas transparent, including the fundamental concept of simultaneously considering both the object space and feature space representations of the data objects. Key ideas are illustrated with a very simple two- dimensional toy example that allows explicit visualizations of both spaces. The concept of modes of variation is formally defined in a way that enables extension in a meaningful way to the case of non-Euclidean data objects. Scree plots, which display relationships between modes in terms of proportions of variation explained are introduced. Mathematical notation, used through the rest of the book, is also defined. Finally, an overview of the intuitive utility of the object and feature space concepts is given. The importance of careful choice of data objects is demonstrated in the specific context of probability distributions as data objects.
