Journal
JOURNAL OF CLASSIFICATION
Volume 26, Issue 2, Pages 227-245Publisher
SPRINGER
DOI: 10.1007/s00357-009-9032-1
Keywords
Indices of association; Resemblance measures; Simple matching coefficient; Jaccard coefficient; Dice/Sorenson coefficient; Rand index; Global order equivalence
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k-Adic formulations (for groups of objects of size k) of a variety of 2-adic similarity coefficients (for pairs of objects) for binary (presence/absence) data are presented. The formulations are not functions of 2-adic similarity coefficients. Instead, the main objective of the the paper is to present k-adic formulations that reflect certain basic characteristics of, and have a similar interpretation as, their 2-adic versions. Two major classes are distinguished. The first class is referred to as Bennani-Heiser similarity coefficients, which contains all coefficients that can be defined using just the matches, the number of attributes that are present and that are absent in k objects, and the total number of attributes. The coefficients in the second class can be formulated as functions of Dice's association indices.
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