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A Note on the Graphical Representation of Multivariate Binary Data
Author(s) -
Banfield C. F.,
Gower J. C.
Publication year - 1980
Publication title -
journal of the royal statistical society: series c (applied statistics)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.205
H-Index - 72
eISSN - 1467-9876
pISSN - 0035-9254
DOI - 10.2307/2346897
Subject(s) - ordination , binary number , representation (politics) , table (database) , dimension (graph theory) , similarity (geometry) , mathematics , simple (philosophy) , binary data , cluster analysis , function (biology) , combinatorics , algorithm , multivariate statistics , computer science , discrete mathematics , statistics , data mining , arithmetic , artificial intelligence , politics , political science , law , philosophy , epistemology , evolutionary biology , biology , image (mathematics)
S ummary Various ordination methods for mapping n units characterized by v binary variables are in common use in which the distance between points P i and P j , representing units i and j , approximates some function (a similarity coefficient) of ( a ij , b ij , c ij , d ij ) , the usual cell‐counts in a 2 × 2 table. Ordination generally requires (n – 1) dimensions to represent the distances exactly, but the quantities b ij ‐ c ij can always be represented in one dimension. This leads to a simple graphical extension of ordination that helps with interpretation, reveals discrepancies, screens clustering possibilities and permits the recovery of approximations to all the ( a, b, c, d )‐values. Two examples illustrate the technique.