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.
Read more about this topic: Kendall Tau Distance
Famous quotes containing the word definition:
“The very definition of the real becomes: that of which it is possible to give an equivalent reproduction.... The real is not only what can be reproduced, but that which is always already reproduced. The hyperreal.”
—Jean Baudrillard (b. 1929)
“Mothers often are too easily intimidated by their children’s negative reactions...When the child cries or is unhappy, the mother reads this as meaning that she is a failure. This is why it is so important for a mother to know...that the process of growing up involves by definition things that her child is not going to like. Her job is not to create a bed of roses, but to help him learn how to pick his way through the thorns.”
—Elaine Heffner (20th century)
“Scientific method is the way to truth, but it affords, even in
principle, no unique definition of truth. Any so-called pragmatic
definition of truth is doomed to failure equally.”
—Willard Van Orman Quine (b. 1908)