Ulam distance measure disorder of ordinal variables by counting the minimum number of *Delete-Shift-Insert* operations.

The algorithm to compute Ulam distance is to count the *minimum * number of operation *Delete-Shift-Insert *:

*Take or delete any single digit*on disorder-vector that does not match to the corresponding digit in pattern-vector.*Shift*the remaining digit on disorder-vector to remove the empty space*Shift*an empty space on disorder-vector that match to the corresponding digit in pattern-vector.*Put or Insert*back the deleted digit the empty space

**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 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 Ulam 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 Ulam 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 any pair to make disorder-vector into pattern-vector. Diagram below show the steps. Since we count two number of the operation *Delete-Shift-Insert*, thus the Ulam distance between A and B is 2.

**Preferable reference for this tutorial is**

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