 

Kendall Distance Kendal distance measure disorder of ordinal variables by counting the minimum number of transposition of discordant pair. Discordant pair is adjacent pair digits on disordervectors that at least one digit does not match to the patternvector. The algorithm to compute Kendal distance is to count the minimum number of operation “ Interchange ” or transposition of discordant pair:
The problem of Kendall distance computation is to find the minimum operation rather than the transposition operation itself.
Example: 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 patternvector and vector B=[Van, Bus, Train] as disordervector. Diagram below shows only single “interchange” operation is needed to transform disordervector into patternvector. Thus, the Kendal distance of preference between A and B is 1
Example: 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 patternvector and vector B as disordervector. Our goal is to count the minimum number of steps of operation “ Interchange ” of discordant pair to make disordervector into patternvector. 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
Preferable reference for this tutorial is Teknomo, Kardi. Similarity Measurement. http:\\people.revoledu.com\kardi\ tutorial\Similarity\




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