How to calculate the similarity of an asymmetric binary variable using Jaccard coefficient?
There are many methods to calculate the similarity of data. Jaccard coefficient is one of them.
Jaccard coefficient is used to calculate the similarity among asymmetric binary attributes.
Contingency table for binary data:
|Object 1|| ||1 / True / Positive||0 / False / Negative||Sum|
|1 / True / Positive||A||B||A + B|
|0 / False / Negative||C||D||C + D|
|Sum||A + C||B + D|| |
In table 1 we can consider the following facts.
A represents that object 1 is True and object 2 is also True.
B represents that object 1 is True and object 2 is False.
C represents that object 1 is False and object 2 is True.
D represents that object 1 is False and object 2 is also False.
|Name||Fever||Cough||Test 1||Test 2||Test 3||Test 4|
|Asad||Negative||Yes|| Negative|| Positive|| Negative|| Negative|
|Bilal||Negative|| Yes|| Negative||Positive|| Positive|| Negative|
|Tahir||Positive||Yes|| Negative|| Negative|| Negative|| Negative|
In table 2, Asad, Bilal and Tahir are objects. Negative values represents False and Positive represents Negative.
Consider 1 for positive/True and 0 for negative/False.
Similarly, we can calculate the similarity of one object with each other object.