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Kendall Distance


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Kendal distance measure disorder of ordinal variables by counting the minimum number of transposition of discordant pair. Discordant pair is adjacent pair digits on disorder-vectors that at least one digit does not match to the pattern-vector.

The algorithm to compute Kendal distance is to count the minimum number of operation Interchange or transposition of discordant pair:

  1. Select adjacent pair on disorder vector that at least one of digit does not match to the corresponding digit in pattern vector (= discordant pair).
  2. Interchange the order of the pair

The problem of Kendall distance computation is to find the minimum operation rather than the transposition operation itself.


We have ask two persons, A and B about their preference on public transport and here is their ordering vector A = [Bus, Van, Train] and B =[Van, Bus, Train]

Suppose we use vector A = [Bus, Van, Train] as pattern-vector and vector B=[Van, Bus, Train] as disorder-vector. Diagram below shows only single interchange operation is needed to transform disorder-vector into pattern-vector. Thus, the Kendal distance of preference between A and B is 1




Suppose we have two judges (A and B) who give rank of importance over 6 products. The ranking vector is given as follow A=[1, 2, 3, 4, 5, 6] and B = [2, 5, 3, 1, 4, 6]. We want to measure Kendall distance between A and B

We set rank vector A as pattern-vector and vector B as disorder-vector. Our goal is to count the minimum number of steps of operation Interchange of discordant pair to make disorder-vector into pattern-vector. Diagram below show the steps. Since we count five number of interchange, thus the Kendall distance between A and B is 5.


See also: Cayley distance

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Teknomo, Kardi (2015) Similarity Measurement. http:\people.revoledu.comkardi tutorialSimilarity

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