Footrule Distance

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Footrule distance is an absolute distance between two rank vectors. Basically, it is similar to the city block distance or Manhattan distance that used for quantitative variables, but Footrule distance is used for rank.

Other name: Spearman footrule distance

Formula

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 set [Bus, Van, Train] as pattern-vector we get rank vector A=[1, 2, 3] and B = [2, 1, 3]. Thus, we can represent the two vectors as two points in three-dimensional space. Point A has coordinate (1, 2, 3) and point B has coordinate (2, 1, 3).

The Footrule distance of preference between A and B is

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Teknomo, Kardi. Similarity Measurement. http:\\people.revoledu.com\kardi\ tutorial\Similarity\