4.2 Article

k-Adic Similarity Coefficients for Binary (Presence/Absence) Data

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JOURNAL OF CLASSIFICATION
卷 26, 期 2, 页码 227-245

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SPRINGER
DOI: 10.1007/s00357-009-9032-1

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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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