Classiication and Learning of Similarity Measures

The background of this paper is the area of case-based reasoning. This is a reasoning technique where one tries to use the solution of some problem which has been solved earlier in order to obtain a solution of a given problem. As example of types of problems where this kind of reasoning occurs very often is the diagnosis of diseases or faults in technical systems. In abstract terms this reduces to a classiication task. A diiculty arises when one has not just one solved problem but when there are very many. These are called \cases" and they are stored in the case-base. Then one has to select an appropriate case which means to nd one which is \similar" to the actual problem. The notion of similarity has raised much interest in this context. We will rst introduce a mathematical framework and deene some basic concepts. Then we will study some abstract phenomena in this area and nally present some methods developed and realized in a system at the University of Kaiserslautern.