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

  • Authors:
  • Matthijs J. Warrens

  • Affiliations:
  • Leiden University, Psychometrics and Research Methodology Group, Leiden University Institute for Psychological Research, P.O. Box 9555, Wassenaarseweg 52, 2300 RB, Leiden, The Netherlands

  • Venue:
  • Journal of Classification
  • Year:
  • 2009

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Abstract

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.