Distance for Binary Variables

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We often face variables that only binary value such as Yes and No, or Agree and Disagree, True and False, Success and Failure, 0 and 1, Absence or Present, Positive and Negative, etc. For such binary variables, there are only two possible values, which can be represented as positive and negative. Similarity of dissimilarity (distance) of two objects that represented by binary variables can be measured in term of number of occurrence (frequency) of positive and negative in each object.

For example:

The coordinate of Apple is (1,1,1,1) and coordinate of Banana is (0,1,0,0). Because each object is represented by 4 variables, we say that these objects has 4 dimensions.

Let

= number of variables that positive for both objects

= number of variables that positive for the th objects and negative for the th object

= number of variables that negative for the th objects and positive for the th object

= number of variables that negative for both objects

= total number of variables

For our example above, we have measured Apple and Banana have , and , . Thus,

The most common use of binary dissimilarity (distance) is

1. Simple Matching distance
2. Jaccard's distance
3. Hamming distance

B.S. Everit (1978) listed 10 other similarity measures for presence-absence data that have been proposed

1. = simple matching coefficient
2. 
3. = Jaccard's coefficient
4. 
5. 
6. 
7. 
8. 
9. 
10. 

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Preferable reference for this tutorial is

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