Cosine similarity [1][2] is a measure of similarity between two vectors of n dimensions by finding the cosine of the angle between them, often used to compare documents in text mining. Given two vectors of attributes, A and B, the cosine similarity, θ, is represented using a dot product and magnitude as
For text matching, the attribute vectors A and B are usually the term frequency vectors of the documents. The cosine similarity can be seen as a method of normalizing document length during comparison.
The resulting similarity ranges from −1 meaning exactly opposite, to 1 meaning exactly the same, with 0 indicating independence, and in-between values indicating intermediate similarity or dissimilarity.
In the case of information retrieval, the cosine similarity of two documents will range from 0 to 1, since the term frequencies (tf-idf weights) cannot be negative. The angle between two term frequency vectors cannot be greater than 90°.
This cosine similarity metric may be extended such that it yields the Jaccard coefficient in the case of binary attributes. This is the Tanimoto coefficient, T(A, B), represented as
See also
- Sørensen's quotient of similarity
- Mountford's index of similarity
- Hamming distance
- Correlation
- Dice's coefficient
- Jaccard index
- SimRank
- Information retrieval
- Weighted cosine measure
References
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