在二维数组中查找到最近邻居的距离

Question

I have a 2D array and I want to find for each (x, y) point the distance to its nearest neighbor as fast as possible.

I can do this using scipy.spatial.distance.cdist :

import numpy as np
from scipy.spatial.distance import cdist

# Random data
data = np.random.uniform(0., 1., (1000, 2))
# Distance between the array and itself
dists = cdist(data, data)
# Sort by distances
dists.sort()
# Select the 1st distance, since the zero distance is always 0.
# (distance of a point with itself)
nn_dist = dists[:, 1]

This works, but I feel like its too much work and KDTree should be able to handle this but I'm not sure how. I'm not interested in the coordinates of the nearest neighbor, I just want the distance (and to be as fast as possible).

Answer 1

KDTree can do this. The process is almost the same as when using cdist. But cdist is much faster. And as pointed out in the comments, cKDTree is even faster:

import numpy as np
from scipy.spatial.distance import cdist
from scipy.spatial import KDTree
from scipy.spatial import cKDTree
import timeit

# Random data
data = np.random.uniform(0., 1., (1000, 2))

def scipy_method():
    # Distance between the array and itself
    dists = cdist(data, data)
    # Sort by distances
    dists.sort()
    # Select the 1st distance, since the zero distance is always 0.
    # (distance of a point with itself)
    nn_dist = dists[:, 1]
    return nn_dist

def KDTree_method():
    # You have to create the tree to use this method.
    tree = KDTree(data)
    # Then you find the closest two as the first is the point itself
    dists = tree.query(data, 2)
    nn_dist = dists[0][:, 1]
    return nn_dist

def cKDTree_method():
    tree = cKDTree(data)
    dists = tree.query(data, 2)
    nn_dist = dists[0][:, 1]
    return nn_dist

print(timeit.timeit('cKDTree_method()', number=100, globals=globals()))
print(timeit.timeit('scipy_method()', number=100, globals=globals()))
print(timeit.timeit('KDTree_method()', number=100, globals=globals()))

Output:

0.34952507635557595
7.904083715193579
20.765962179145546

Once again, then very unneeded proof that C is awesome!