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Generalized proximity function comparisons
Author(s) -
Hubert Lawrence J.
Publication year - 1978
Publication title -
british journal of mathematical and statistical psychology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.157
H-Index - 51
eISSN - 2044-8317
pISSN - 0007-1102
DOI - 10.1111/j.2044-8317.1978.tb00583.x
Subject(s) - cartesian product , mathematics , permutation (music) , cross product , test statistic , product (mathematics) , statistic , partition (number theory) , function (biology) , variety (cybernetics) , seriation (archaeology) , set (abstract data type) , simple (philosophy) , statistics , computer science , statistical hypothesis testing , discrete mathematics , combinatorics , philosophy , physics , geometry , epistemology , evolutionary biology , acoustics , biology , programming language , history , archaeology
Generalizations are given for a simple cross‐product statistic that has been used to compare two proximity functions defined on the Cartesian product of a given set S. The extensions developed here are based on a similar cross‐product form but rely on two functions defined either on S × S × S or on S × S × S × S. Typically, the latter are obtained in some way from the original proximity measures. A variety of these indices, suggested by the recent literature on cluster analysis and seriation, are mentioned explicitly along with a discussion of an approximate permutation test for assessing their relative size. Finally, a representative application of two generalized cross‐product statistics is presented in terms of a data analysis problem that requires the comparison of a partition of S against a proximity function denned on S × S.