Ordinal network representation: Representing proximities by graphs |
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Authors: | Karl Christoph Klauer |
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Affiliation: | (1) FU Berlin, Institut für Psychologie, Habelschwerdter Allee 45, 1000 Berlin 33, FRG |
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Abstract: | Ordinal network representations are graph-theoretic representations of proximity data. They seek to provide parsimonious representations of the ordinal (nonmetric) information in observed proximity data by means of the minimum-path-length distance of a connected and weighted graph. In contrast to traditional tree-based graph-theoretic approaches, ordinal network representation is not limited to but includes the representation by trees. Asymmetry in the proximity data and violations of zero-minimality are allowed for. The paper explores fundamental representation and uniqueness results and discusses a method of constructing ordinal network representations. A simple strategy for handling the problem of errors in the data is described and illustrated.This work was supported by grant Fe 75/20-2 of the Deutsche Forschungsgemeinschaft. The author is indebted to Hubert Feger for many inspiring discussions. |
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Keywords: | proximity graph-theoretic representation addtrees extended similarity trees hierarchical clustering |
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