How to calculate proximity measure for asymmetric binary attributes?
In this tutorial, we will learn about the proximity measure for asymmetric binary attributes
Contingency table for binary data
Here in this example, consider 1 for positive/True and 0 for negative/False.
|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 also False.
C represents that object 1 is False and object 2 is also 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.
In the results, we can see the following facts;
The distance between object 1 and 2 is 0.67. Asad is object 1 and Tahir is in object 2 and the distance between both is 0.67.
Less distance is between Asad and Bilal. It means that Asad and Bilal are more similar to each other as compared to other objects.