Advanced Similarity Topics

Abstract

This advanced chapter is addressed to readers who are interested in foundational aspects, formal aspects, subjectivity, functional dependency, and other special additional problems. The general aspects of similarities are extended and deepened. We introduce a semantics for similarity measures allowing us to define correctness for similarity-based computation. The first part of this chapter discusses the concept of semantics, i.e., the meaning of similarity measure. The semantic is based on utility and allows formal specifications. As a consequence, one can talk about the correctness of similarity computations. This allows also for discussing several possible axiomatic properties. Often, the utility is unknown and/or not formally defined. For this purpose, subjectivity is investigated. In order to compare similarity measures from an abstract point of view, we study the knowledge contained in the measure. For constructing a measure, we compare a bottom-up and a top-down approach. The introduction of weight diversity helps in choosing weights. The second part of this chapter discusses several aspects that can influence the use of similarity as noise, or as missing or redundant values. We show the problems and indicate possibilities to handle them. Besides finding a solution, the use of similarities relates to other tasks and methods. We discuss logical inferences and explanations. Familiarity with Part I and Chaps. 6 and 7 on similarity is recommended.