It looks like scipy.spatial.distance.cdist cosine similariy distance:
1 - u*v/(||u||||v||)
is different from sklearn.metrics.pairwise.cosine_similarity which is
u*v/||u||||v||
Does anybody know reason for different definitions?
14
votes
The link that you labeled "link to cos similarity 1" is not cosine similarity, and it is not called that in the link. It is cosine distance.
- Warren Weckesser
Think of the trivial case: distance(X, X) should be 0, because the distance from X to X is 0. similarity(X, X) should be the maximum of the function that measures similariy (1 in this case), because X and X are as similar as two things can be.
- Warren Weckesser
@WarrenWeckesser, thank you, I fixed the name.
- user1700890
1 Answers
23
votes
Good question but yes, these are 2 different things but connected by the following equation:
Cosine_distance = 1 - cosine_similarity
Why?
Usually, people use the cosine similarity as a similarity metric between vectors. Now, the distance can be defined as 1-cos_similarity.
The intuition behind this is that if 2 vectors are perfectly the same then similarity is 1 (angle=0) and thus, distance is 0 (1-1=0).
Similarly you can define the cosine distance for the resulting similarity value range.
Cosine similarity range: −1 meaning exactly opposite, 1 meaning exactly the same, 0 indicating orthogonality.
