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scipycosine-similarity

What is the cosine distance of something and itself?

I'm playing with scipy's cosine distance. From what I've gathered, the closer a cosine distance is to 1, the more similar the vectors are. I got some unexpected results in a text mining project, so I decided to investigate the simplest case.

import numpy as np
import scipy.spatial
arr1 = np.array([1,1])
arr2 = np.array([1,1])
print scipy.spatial.distance.cosine(arr1, arr2)

My program prints 0.0.

Shouldn't the result be 1.0? Why or why not?

Solution

  • It is the cosine distance, not the cosine similarity. A basic requirement for a function d(u, v) to be a distance is that d(u, u) = 0.

    See the definition of the formula in the docstring of scipy.spatial.distance.cosine, and notice that the formula begins 1 - (...). Your expectation of the function is probably based on the quantity in (...), but that expression is the cosine similarity.