Learning Complex Similarity Measures

Case-based reasoning is a knowledge processing concept that has shown success in various problem classes. One key challenge in CBR is the construction of a measure that adequately models the similarity between two cases. Typically, a similarity measure consists of a set of feature-specific distance functions coupled with an underlying feature weighting (importance) scheme. While the definition of the distance functions is often straightforward, the estimation of the weighting scheme requires a deep understanding of the domain and the underlying connections. The paper in hand addresses this problem. It shows how discrimination knowledge, which is coded within an already solved classification problem, can be transformed towards a similarity measure. Moreover, it demonstrates our approach at the problem of diagnosing heart diseases. 1 Background and Related Theory Discrimination knowledge that is coded within an already solved classification problem can be transformed towards a similarity measure of a case-based reasoning (CBR) system. This chapter first points out relationships between classification and similarity assessment in a case-based reasoning system. It then motivates and defines a generic transformation procedure from a case base to a similarity measure; the last two sections of this chapter discuss related realizational aspects. Chapter 2 presents an application, the diagnosis of heart diseases, to demonstrate the development of a similarity measure at a real-world problem. 1.1 Classification and Case-based Reasoning Let x denote a problem or some description of a situation. Then a common task is to find another problem y amongst a set S of problems, such that y is more similar to x than it is to any other z ∈ S. Using the terminology of case-based reasoning, we are given a pair 〈CB, sim〉, where CB, the case base, denotes a set of cases, and sim denotes a similarity measure, sim : CB × CB → [0, 1]. With x, y, and z ∈ CB the semantics of sim is as follows. sim(x, y) > sim(x, z) ⇔ “x is more similar to y than it is to z.”