Geometric Similarity Metrics for Case-Based Reasoning

TL;DRAbstract

Case-based reasoning is a problem solving method that uses stored solutions to problems to aid in solving similar new problems. One of the difficulties of case-based reasoning is identifying cases that are relevant to a problem. If the problem is defined on a geometric domain --- for instance, planning a route using a city map --- it becomes possible to take advantage of the geometry to simplify the task of finding appropriate cases. We propose a methodology for determining a set of cases which collectively forms a good basis for a new plan, and may include partial cases, unlike most existing similarity metrics. This methodology is applicable in continuous-valued domains, where one cannot rely on the traditional method of simple role-substitution and matching. Theproblem of identifying relevant cases is transformed into a geometric problem with an exact solution. We construct two similar algorithms for solving the geometric problem. The first algorithm returns a correct solution, but i

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