On realizable biorders and the biorder dimension of a relation |
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Authors: | Jean-Paul Doignon André Ducamp Jean-Claude Falmagne |
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Affiliation: | Université Libre de Bruxelles Belgium;New York University USA |
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Abstract: | The paper discusses the mathematical foundations of a technique of multidimensional scaling, generalizing Guttman scaling, in which the structure of the embedding space relies only on ordinal concepts. An empirical relation is represented as an intersection of a minimal number (called bidimension) of Guttman relations. Fairly complete results are given for the cases of bidimensions 1 and 2. In the general case, the main results are based on the equivalence between the bidimension and the dimension of a certain partial order. A characterization of the bidimension as the chromatic number of some hypergraph is also provided. |
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Keywords: | Address reprints requests to J.-P. Doignon Université Libre de Bruxelles C.P. 216 Bd du Triomphe 1050 Bruxelles Belgium. |
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