Summary
In this chapter, we analyze and discuss the concept of similarity. Similarity plays an important role in many computer applications. These are often tasks that have either no precise input description or where the solution can only be approximated. We consider two main methodologies, case-based reasoning (CBR) and pattern recognition (PR). The specific tasks we deal with are mainly classification, diagnosis, image understanding, and information retrieval. The way similarity enters such scenarios is quite diverse and therefore we will present a relatively broad investigation of similarity relations and measures. When solving a task, similarity is not the only concept that is used; therefore, the overall process and its methods have to be considered. That means, besides the syntax of similarity concepts we discuss also the meaning and the semantics. For this, the semantics is ultimately reduced to utility.
In order to solve problems some knowledge is necessary. This knowledge has different sources and can be used in different ways. Therefore, we put some emphasis on the question what kind of knowledge is needed, what is contained in a measure and how is it entered into a system. This is quite different in CBR and PR. Here we make use of the concept of knowledge containers and of the local-global principle.
For illustration, we also present many examples of problems, measures, and application types. Because of the diverging terminology we are also heading toward a unified view on the subject.