Calculate Distances Between One Point in Matrix From All Other Points

Question

I am new to Python and I need to implement a clustering algorithm. For that, I will need to calculate distances between the given input data.

Consider the following input data -

    [[1,2,8],
     [7,4,2],
     [9,1,7],
     [0,1,5],
     [6,4,3]]

What I am looking to achieve here is, I want to calculate distance of [1,2,8] from ALL other points, and find a point where the distance is minimum.

And I have to repeat this for ALL other points.

I am trying to implement this with a FOR loop, but I am sure that SciPy/ NumPy must be having a function which can help me achieve this result efficiently.

I looked online, but the 'pdist' command could not get my work done.

Can someone guide me?

TIA

Answer 1

Use np.linalg.norm combined with broadcasting (numpy outer subtraction), you can do:

np.linalg.norm(a - a[:,None], axis=-1)

a[:,None] insert a new axis into a, a - a[:,None] will then do a row by row subtraction due to broadcasting. np.linalg.norm calculates the np.sqrt(np.sum(np.square(...))) over the last axis:

---

a = np.array([[1,2,8],
     [7,4,2],
     [9,1,7],
     [0,1,5],
     [6,4,3]])

np.linalg.norm(a - a[:,None], axis=-1)
#array([[ 0.        ,  8.71779789,  8.1240384 ,  3.31662479,  7.34846923],
#       [ 8.71779789,  0.        ,  6.164414  ,  8.18535277,  1.41421356],
#       [ 8.1240384 ,  6.164414  ,  0.        ,  9.21954446,  5.83095189],
#       [ 3.31662479,  8.18535277,  9.21954446,  0.        ,  7.        ],
#       [ 7.34846923,  1.41421356,  5.83095189,  7.        ,  0.        ]])

The elements [0,1], [0,2] for instance correspond to:

np.sqrt(np.sum((a[0] - a[1]) ** 2))
# 8.717797887081348

np.sqrt(np.sum((a[0] - a[2]) ** 2))
# 8.1240384046359608

respectively.