Abstract
Generalized cases are cases that cover a subspace rather than a point in the problem-solution space. Generalized cases can be represented by a set of constraints over the case attributes. For such representations, the similarity assessment between a point query and generalized cases is a difficult problem that is addressed in this paper. The task is to find the distance (or the related similarity) between the point query and the closest point of the area covered by the generalized cases, with respect to some given similarity measure. We formulate this problem as a mathematical optimization problem and we propose a new cutting plane method which enables us to rank generalized cases according to their distance to the query.
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References
M. Avriel and B. Golany. Mathematical Programming for Industrial Engineers. Marcel Dekker, INC., 1996.
Ray Bareiss. Exemplar-Based Knowledge Acquisition: A unified Approach to Concept Representation, Classification and Learning. Academic Press, 1989.
M. S. Bazaraa, H.D. Sherali, and Shetty C.M. NonLinear Programming, Theorey and Algorithms. 2nd Edition, Wiley, 1993.
R. Bergmann. Experience Management: Foundations, Development Methodology, and Internet-based Applications. Springer, forthcomming, 2002.
R. Bergmann and I. Vollrath. Generalized cases: Representation and steps towards efficient similarity assessment. In W. Burgard, Th. Christaller, and A. B. Cremers, editors, KI-99: Advances in Artificial Intelligence., LNAI 1701. Springer, 1999.
R. Bergmann, I. Vollrath, and T. Wahlmann. Generalized cases and their application to electronic designs. In E. Melis, editor, 7. German Workshop on Case-Based Reasoning (GWCBR’99)., 1999.
Ralph Bergmann. Effizientes Problemlösen durch flexible Wiederverwendung von Fällen auf verschiedenen Abstraktions ebenen. DISKI 138. infix, 1996.
L. Blum, F. Cucker, M. Shub, and Smale S. Complexity and Real Computation. Springer, 1997.
H.-D. Burkhard and M.M. Richter. Similarity in case-based reasoning and fuzzy theory. In S.K. Pal, T.S. Dillon, and D.S. Yeung, editors, Soft Computing in Case-Based Reasoning, chapter 2. Springer, 2000.
R. Horst and H. Tuy. Global Otimization: Deterministic Approaches. Springer, 1993.
Kefeng Hua, Ian Smith, and Boi Faltings. Integrated case-based building design. In Stefan Wess, Klaus-Dieter Althoff, and Michael M Richter, editors, Topics in Case-Based Reasoning. Proc. Of the First European Workshop on Case-Based Reasoning (EWCBR-93), Lecture Notes in Artificial Intelligence, 837, pages 436–445. Springer Verlag, 1993.
Janet L Kolodner. Retrieval and Organizational Strategies in Conceptual Memory. PhD thesis, Yale University, 1980.
Jeff Lewis. Intellectual property (IP) components. Artisan Components, Inc., [web page], http://www.artisan.com/ip.html, 1997. [Accessed 28 Oct 1998].
B. Mougouie. Optimization of distance/similarity functions under linear and nonlinear constraints with application in case-based reasoning. Diplomarbeit, Max-Planck Institut für Informatik, Saarbrücken, Germany., 2001.
S. Nickel. Convex analysis. Technical report, Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany, 1998.
L. Portinale, P. Torasso, and D. Magro. Selecting most adaptable diagnostic solutions thorugh pivoting-based retrieval. In David B Leake and Enric Plaza, editors, Case-Based Reasoning Research and Development, Proc. ICCBR-97, Lecture Notes in Artificial Intelligence, 1266, pages 393–402. Springer Verlag, 1997.
Lisa Purvis and Pearl Pu. Adaptation using constraint satisfaction techniques. Lecture Notes in Artificial Intelligence, 1010, pages 289–300. Springer Verlag, 1995.
S Salzberg. A nearest hyperrectangle learning method. Machine Learning, 6:277–309, 1991.
Jörg W. Schaaf. Fish and shrink: a next step towards efficient case retrieval in large scaled case bases. In Ian Smith and Boi Faltings, editors, Advances in Case-Based Reasoning, Lecture Notes in Artificial Intelligence, 1186, pages 362–376. Springer Verlag, 1996.
A. Schoebel. Lecture notes in location theory. Technical report, Department of Mathematics, University of Kaiserslautern, Kaiserslautern, Germany, 2000.
Thomas Wahlmann. Implementierung einer skalierbaren diskreten Kosinustransformation in VHDL. Diploma thesis, University of Siegen, 1999.
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Mougouie, B., Bergmann, R. (2002). Similarity Assessment for Generalizied Cases by Optimization Methods. In: Craw, S., Preece, A. (eds) Advances in Case-Based Reasoning. ECCBR 2002. Lecture Notes in Computer Science(), vol 2416. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-46119-1_19
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DOI: https://doi.org/10.1007/3-540-46119-1_19
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