Using k-d Trees to Improve the Retrieval Step in Case-Based Reasoning

Retrieval of cases is one important step within the case-based reasoning paradigm. We propose an improvement of this stage in the process model for nding most similar cases with an average eeort of Olog2n], n number of cases. The basic idea of the algorithm is to use the heterogeneity of the search space for a density-based structuring and to employ this precomputed structure, a k-d tree, for eecient case retrieval according to a given similarity measure sim. In addition to illustrating the basic idea, we present the experimental results of a comparison of four diierent k-d tree generating strategies as well as introduce the notion of virtual bounds as a new one that signiicantly reduces the retrieval eeort from a more pragmatic perspective. The presented approach is fully implemented within the (Patdex) system, a case-based reasoning system for diagnostic applications in engineering domains.