One-to-One Correspondence Between Indexed Cluster Structures and Weakly Indexed Closed Cluster Structures
Chapter
Abstract
We place ourselves in a setting where singletons are not all required to be clusters, and we show that the resulting cluster structures and their corresponding closure under finite nonempty intersections still have the same minimal members. Moreover, we show that indexed cluster structures and weakly indexed closed cluster structures correspond in a one-to-one way.
Keywords
Nonempty Subset Cluster Structure Order Preserve Nonempty Intersection Additive Cluster
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Preview
Unable to display preview. Download preview PDF.
References
- BANDELT, H.-J. and DRESS, A.W.M. (1989): Weak hierarchies associated with similarity measures: an additive clustering technique. Bull. Math. Biology 51, 113–166.Google Scholar
- BATBEDAT, A. (1988): Les isomorphismes HTS et HTE (après la bijection de Benzécri/Johnson) (première partie). Metron 46, 47–59.MATHGoogle Scholar
- BERTRAND, P. (2000): Set Systems and Dissimilarities. Europ. J. Combinatorics 21, 727–743.MATHCrossRefGoogle Scholar
- DIATTA, J. and FICHET, B. (1994): From Apresjan hierarchies and Bandelt-Dress weak hierarchies to quasi-hierarchies. In: E. Diday, Y. Lechevalier, M. Schader, P. Bertrand and B. Burtschy (Eds.): New Approaches in Classification and Data Analysis. Springer-Verlag, 111–118.Google Scholar
- DIDAY, E. (1984): Une représentation visuelle des classes empiétantes: les pyramides. Technical Report 291, INRIA, France.Google Scholar
- DURAND, C. and FICHET, B. (1988): One-to-one correspondences in pyramidal representation: a unified approach. In H. H. Bock (Ed.): Classification and Related Methods of Data Analysis. North-Holland, Amsterdam, 85–90.Google Scholar
Copyright information
© Springer-Verlag Berlin Heidelberg 2007