Basic Similarity Topics

Abstract

Chapter 6 is intended to give the reader a first advice on which similarity measure is suitable for which task, when designing a CBR system. For this purpose, it contains the basic material necessary for understanding and building simple similarity measures. Similarity assessment is a substep of the retrieve process step and is responsible for identifying potentially useful cases from the case base. Because usefulness depends on the user’s context there is no universal method to define similarity. In order to understand the most suitable methods, this chapter gives a general overview of different concepts connected with similarity, including mathematical models of similarity. We discuss the difference between relational and functional similarity, and the important nearest neighbour concept, then list a variety of elementary measures that differ only partially but are used frequently. Some of the measures discussed are counting measures, structure-oriented, and transformational. These approaches are unified by introducing the local-global principle from case representations for similarity measures too. This principle relates object representations and measures. In constructing a similarity measure, a basic difficulty is finding the values for weights. The approach presented formalizes weights on the basis of their predictive power. This approach is also used for defining the independence of attributes. The problem of dependent attributes is approached by introducing virtual attributes. This chapter assumes understanding of Part I and Chap. 5, Case Representations. Similarity is also discussed in Chap. 7, where complex topics are discussed. In later chapters we will occasionally mention similarity when describing topics such as fuzzy sets, random variables and texts.