Python - How to generate the Pairwise Hamming Distance Matrix

Question

beginner with Python here. So I\'m having trouble trying to calculate the resulting binary pairwise hammington distance matrix between the rows of an input matrix using only th

Answer 1

Try this approach, create a new axis along axis = 1, and then do broadcasting and count trues or non zero with sum:

(arr[:, None, :] != arr).sum(2)

# array([[0, 2, 3],
#        [2, 0, 3],
#        [3, 3, 0]])

---

def compute_HammingDistance(X):
    return (X[:, None, :] != X).sum(2)

Explanation:

1) Create a 3d array which has shape (3,1,6)

arr[:, None, :]
#array([[[1, 0, 0, 1, 1, 0]],
#       [[1, 0, 0, 0, 0, 0]],
#       [[1, 1, 1, 1, 0, 0]]])

2) this is a 2d array has shape (3, 6)

arr   
#array([[1, 0, 0, 1, 1, 0],
#       [1, 0, 0, 0, 0, 0],
#       [1, 1, 1, 1, 0, 0]])

3) This triggers broadcasting since their shape doesn't match, and the 2d array arr is firstly broadcasted along the 0 axis of 3d array arr[:, None, :], and then we have array of shape (1, 6) be broadcasted against (3, 6). The two broadcasting steps together make a cartesian comparison of the original array.

arr[:, None, :] != arr 
#array([[[False, False, False, False, False, False],
#        [False, False, False,  True,  True, False],
#        [False,  True,  True, False,  True, False]],
#       [[False, False, False,  True,  True, False],
#        [False, False, False, False, False, False],
#        [False,  True,  True,  True, False, False]],
#       [[False,  True,  True, False,  True, False],
#        [False,  True,  True,  True, False, False],
#        [False, False, False, False, False, False]]], dtype=bool)

4) the sum along the third axis count how many elements are not equal, i.e, trues which gives the hamming distance.