An Optimal Footprint Method for Case-Base Maintenance

In Case-Based Reasoning (CBR), new problems are solved by retrieving similar previously solved cases and adapting their solutions. The new case is then stored appropriately in the case-base for future use. It is a fundamental problem to control the growth of case-base and the case-base maintenance step retains cases in the case-base based on an estimate of their usefulness in solving new problems. We propose an optimization formulation to identify an optimal set of representative cases called the optimal footprint of the case-base. The optimization formulation ensures that the optimal footprint set strikes a right trade-off between minimizing the number of cases and maximizing their ability to solve the remaining cases in the case-base. This trade-off is studied empirically in this paper. We also illustrate the trade-off between the size and performance of optimal footprint in the context of regression. Introduction Case-Based Reasoning (CBR) (Kolodner 1992) is an experience based learning methodology, which reuses past experiences to solve problems in future. It solves new problems by retrieving and adapting solutions of similar previously solved problems that have been stored in a repository called the case-base (De Mantaras et al. 2005). The case-base contains problem-solution pairs of problems that are solved in the past. For example, in regression data, each data instance corresponds to the problem and its target value corresponds to the solution. Each problem-solution pair is considered as a case in the case-base. The case-base size increases when more previously solved cases are added to the case-base. The size reduction of a case-base is ensured during the Case-Base Maintenance (Reinartz, Iglezakis, and Roth-Berghofer 2001, Smyth 1998) step, which retains cases in the case-base based on its quality to arrive at a solution for new problems. Competence of a case-base (Smyth and McKenna 1998) is the range of target problems that can be solved by the cases in that case-base. The footprint based approach (Smyth and McKenna 1999) is a competence guided case-base maintenance method to estimate a subset of cases in the case-base called the footprint set, which can solve the remaining cases in the case-base. More precisely, the footprint based approach is a data reduction approach in CBR which identifies a set of Copyright c © 2018, Association for the Advancement of Artificial Intelligence (www.aaai.org). All rights reserved. c1 c2 c3 c4