Similarity of Asymmetric Binary Attributes
Given two objects, A and B, each with n binary attributes, the Jaccard coefficient is a useful measure of the overlap that A and B share with their attributes. Each attribute of A and B can either be 0 or 1. The total number of each combination of attributes for both A and B are specified as follows:
- represents the total number of attributes where A and B both have a value of 1.
- represents the total number of attributes where the attribute of A is 0 and the attribute of B is 1.
- represents the total number of attributes where the attribute of A is 1 and the attribute of B is 0.
- represents the total number of attributes where A and B both have a value of 0.
Each attribute must fall into one of these four categories, meaning that
The Jaccard similarity coefficient, J, is given as
The Jaccard distance, J', is given as
Read more about this topic: Jaccard Index
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