cosine distance between two matrices

Question

Take two matrices, arr1, arr2 of size mxn and pxn respectively. I'm trying to find the cosine distance of their respected rows as a mxp matrix. Essentially I want to take the the pairwise dot product of the rows, then divide by the outer product of the norms of each rows.

import numpy as np
def cosine_distance(arr1, arr2):
    numerator = np.dot(arr1, arr2.T)
    denominator = np.outer(
        np.sqrt(np.square(arr1).sum(1)),
        np.sqrt(np.square(arr2).sum(1)))
   return np.nan_to_num(np.divide(numerator, denominator))

I Think this should be returning an mxn matrix with entries in [-1.0, 1.0] but for some reason I'm getting values out of that interval. I'm thinking that my one of these numpy functions is doing something other than what I think it does.

Answer 1

It sounds like you need to divide by the outer product of the L2 norms of your arrays of vectors:

arr1.dot(arr2.T) / np.outer(np.linalg.norm(arr1, axis=1),
                            np.linalg.norm(arr2, axis=1))

e.g.

In [4]: arr1 = np.array([[1., -2., 3.],
                         [0., 0.5, 2.],
                         [-1., 1.5, 1.5],
                         [2., -0.5, 0.]])

In [5]: arr2 = np.array([[0., -3., 1.],
                         [1.5, 0.25, 1.]])

In [6]: arr1.dot(arr2.T)/np.outer(np.linalg.norm(arr1, axis=1),
                                  np.linalg.norm(arr2, axis=1))
Out[6]: 
array([[ 0.76063883,  0.58737848],
       [ 0.0766965 ,  0.56635211],
       [-0.40451992,  0.08785611],
       [ 0.2300895 ,  0.7662411 ]])