Abstract
In [9] we introduced a formal framework for constructing ordinal similarity measures, and suggested how this might also be applied to cardinal measures. In this paper we will place this approach in a more general framework, called similarity metrics. In this framework, ordinal similarity metrics (where comparison returns a boolean value) can be combined with cardinal metrics (returning a numeric value) and, indeed, with metrics returning values of other types, to produce new metrics.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
A. Aamodt and E. Plaza. Case based reasoning: Foundational issues, methodological variations and system approaches. AI Communications, 7(l):39–59, 1994.
K.D. Ashley and E.L. Rissland. A case-based approach to modeling legal expertise. IEEE Expert, 3(3):70–77, 1988.
G. Birkhoff. Lattice Theory. American Mathematical Society, 1967.
M. Fréchet. Sur quelques points du calcul fonctionel. Rendiconti del Circolo Matematico di Palermo, 22:1–74, 1906.
T.R. Hinrichs. Problem Solving in Open Worlds: A Case Study in Design. Lawrence Erlbaum, 1992.
K.P. Jantke. Nonstandard concepts of similarity in case-based reasoning. In H.H. Bock, W. Lenski, and M.M. Richter, editors, Proceedings der Jahrestagung der Gesellschaft für Klassifikation, Information Systems and Data Analysis: Prospects, Foundations, Applications, pages 29–44. Springer Verlag, 1994.
J.L. Kolodner. Case Based Reasoning. Morgan Kaufmann, 1993.
P. Koton. Reasoning about evidence in causal explanations. In Proceedings of AAAI-88, pages 256–261, 1988.
Hugh Osborne and Derek Bridge. A case base similarity framework. In Ian Smith and Boi Faltings, editors, Advances in Case-Based Reasoning, Proceedings of EWCBR'96, pages 309–323, 1996.
Hugh Osborne and Derek Bridge. Similarity metrics: A formal approach to case base retrieval using general similarity metrics. Technical report, Department of Computer Science, University of York, 1997. In preparation.
E. Plaza. Cases as terms: A feature term approach to the structured representation of cases. In Proceedings of the First International Conference on Case-Based Reasoning. Springer Verlag, 1995.
E. Plaza. On the importance of similitude: An entropy-based assessment. In Ian Smith and Boi Faltings, editors, Advances in Case-Based Reasoning, Proceedings of EWCBR'96, pages 324–338, 1996.
M.M. Richter. Classification and learning of similarity measures. In Proceedings der Jahrestagung der Gesellschaft für Klassifikation, Studies in Classification, Data Analysis and Knowledge Organisation. Springer Verlag, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Osborne, H., Bridge, D. (1997). Similarity metrics: A formal unification of cardinal and non-cardinal similarity measures. In: Leake, D.B., Plaza, E. (eds) Case-Based Reasoning Research and Development. ICCBR 1997. Lecture Notes in Computer Science, vol 1266. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-63233-6_495
Download citation
DOI: https://doi.org/10.1007/3-540-63233-6_495
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-63233-7
Online ISBN: 978-3-540-69238-6
eBook Packages: Springer Book Archive