Definition
The Kendall tau distance between two lists and is
will be equal to 0 if the two lists are identical and (where is the list size) if one list is the reverse of the other. Often Kendall tau distance is normalized by dividing by so a value of 1 indicates maximum disagreement. The normalized Kendall tau distance therefore lies in the interval .
Kendall tau distance may also be defined as
where
- P is the set of unordered pairs of distinct elements in and
- = 0 if i and j are in the same order in and
- = 1 if i and j are in the opposite order in and
Kendall tau distance can also be defined as the total number of discordant pairs.
Kendall tau distance in Rankings: A permutation (or ranking) is an array of N integers where each of the integers between 0 and N-1 appears exactly once. The Kendall tau distance between two rankings is the number of pairs that are in different order in the two rankings. For example the Kendall tau distance between 0 3 1 6 2 5 4 and 1 0 3 6 4 2 5 is four because the pairs 0-1, 3-1, 2-4, 5-4 are in different order in the two rankings, but all other pairs are in the same order.
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