How To Calculate Euclidean Distance Between Pair Of Rows Of A Numpy Array

I have a numpy array like: import numpy as np a = np.array([[1,0,1,0], [1,1,0,0], [1,0,1,0], [0,0,1,1]]) I would like to calculate euclidian

Solution 1:

In terms of something more "elegant" you could always use scikitlearn pairwise euclidean distance:

from sklearn.metrics.pairwise import euclidean_distances
euclidean_distances(a,a)

having the same output as a single array.

array([[ 0.        ,  1.41421356,  0.        ,  1.41421356],
       [ 1.41421356,  0.        ,  1.41421356,  2.        ],
       [ 0.        ,  1.41421356,  0.        ,  1.41421356],
       [ 1.41421356,  2.        ,  1.41421356,  0.        ]])

Solution 2:

And for completeness, einsum is often referenced for distance calculations.

a = np.array([[1,0,1,0],
         [1,1,0,0],
         [1,0,1,0],
         [0,0,1,1]])

b = a.reshape(a.shape[0], 1, a.shape[1])

np.sqrt(np.einsum('ijk, ijk->ij', a-b, a-b))

array([[ 0.        ,  1.41421356,  0.        ,  1.41421356],
       [ 1.41421356,  0.        ,  1.41421356,  2.        ],
       [ 0.        ,  1.41421356,  0.        ,  1.41421356],
       [ 1.41421356,  2.        ,  1.41421356,  0.        ]])

Solution 3:

I used itertools.combinations together with np.linalg.norm of the difference vector (this is the euclidean distance):

import numpy as np
import itertools
a = np.array([[1,0,1,0],
              [1,1,0,0],
              [1,0,1,0],
              [0,0,1,1]])

print([np.linalg.norm(x[0]-x[1]) for x in itertools.combinations(a, 2)])

For understanding have a look at this example from the docs: combinations('ABCD', 2) gives AB AC AD BC BD CD. In your case, A, B, C and D are the rows of your matrix a, so the term x[0]-x[1] appearing in the above code is the difference vector of the vectors in the rows of a.