Jaccard similarity

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This is a technical method discussed in Social Media Analysis 10-802 in Spring 2010.

What problem does it address

Quantifying similarity between two vectors. Refers to measuring the angular distance (cosine) between two vectors. In text domains, a document is generally treated as a bag of words where each unique word in the vocabulary is a dimension of the vector. Thus similarity between two documents can be assessed by finding the cosine similarity between the vectors corresponding to these two documents. Each element of vector A and vector B is generally taken to be tf-idf weight.

Algorithm

  • Input

A : Binary Vector 1 B : Binary Vector 2

  • Output

Given two vectors of attributes, A and B, the cosine similarity, θ, is represented using a dot product and magnitude as

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:

Used in

Widely used for calculating the similarity of documents using the bag-of-words and vector space models

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