Finding the closest point to a list of points

I'm trying to find the closest point (Euclidean distance) from a user-inputted point to a list of 50,000 points that I have. Note that the list of points changes all the time. and the closest distance depends on when and where the user clicks on the point.

#find the nearest point from a given point to a large list of points

import numpy as np

def distance(pt_1, pt_2):
    pt_1 = np.array((pt_1[0], pt_1[1]))
    pt_2 = np.array((pt_2[0], pt_2[1]))
    return np.linalg.norm(pt_1-pt_2)

def closest_node(node, nodes):
    pt = []
    dist = 9999999
    for n in nodes:
        if distance(node, n) <= dist:
            dist = distance(node, n)
            pt = n
    return pt

a = []
for x in range(50000):
    a.append((np.random.randint(0,1000),np.random.randint(0,1000)))

some_pt = (1, 2)

closest_node(some_pt, a)

It will certainly be faster if you vectorize the distance calculations:

def closest_node(node, nodes):
    nodes = np.asarray(nodes)
    dist_2 = np.sum((nodes - node)**2, axis=1)
    return np.argmin(dist_2)

There may be some speed to gain, and a lot of clarity to lose, by using one of the dot product functions:

def closest_node(node, nodes):
    nodes = np.asarray(nodes)
    deltas = nodes - node
    dist_2 = np.einsum('ij,ij->i', deltas, deltas)
    return np.argmin(dist_2)

Ideally, you would already have your list of point in an array, not a list, which will speed things up a lot.

StackExchange Code Review Q#28207, answer score: 43