Find all nearest neighbors within a specific distance

Question

I have a large list of x and y coordinates, stored in an numpy array.

Coordinates = [[ 60037633 289492298]
 [ 60782468 289401668]
 [ 60057234 289419794]]
...
...

What I want is to find all nearest neighbors within a specific distance (lets say 3 meters) and store the result so that I later can do some further analysis on the result.

For most packages I found it is necessary to decided how many NNs should be found but I just want all within the set distance.

How can I achieve something like that and what is the fastest and best way to achieve something like that for a large dataset (some million points)?

Solution

You could use a scipy.spatial.cKDTree:

import numpy as np
import scipy.spatial as spatial
points = np.array([(1, 2), (3, 4), (4, 5)])
point_tree = spatial.cKDTree(points)
# This finds the index of all points within distance 1 of [1.5,2.5].
print(point_tree.query_ball_point([1.5, 2.5], 1))
# [0]

# This gives the point in the KDTree which is within 1 unit of [1.5, 2.5]
print(point_tree.data[point_tree.query_ball_point([1.5, 2.5], 1)])
# [[1 2]]

# More than one point is within 3 units of [1.5, 1.6].
print(point_tree.data[point_tree.query_ball_point([1.5, 1.6], 3)])
# [[1 2]
#  [3 4]]

---

Here is an example showing how you can find all the nearest neighbors to an array of points, with one call to point_tree.query_ball_point:

import numpy as np
import scipy.spatial as spatial
import matplotlib.pyplot as plt
np.random.seed(2015)

centers = [(1, 2), (3, 4), (4, 5)]
points = np.concatenate([pt+np.random.random((10, 2))*0.5 
                         for pt in centers])
point_tree = spatial.cKDTree(points)

cmap = plt.get_cmap('copper')
colors = cmap(np.linspace(0, 1, len(centers)))
for center, group, color  in zip(centers, point_tree.query_ball_point(centers, 0.5), colors):
   cluster = point_tree.data[group]
   x, y = cluster[:, 0], cluster[:, 1]
   plt.scatter(x, y, c=color, s=200)

plt.show()

Comments

[askewchan]

I believe it's recommended to use spatial.cKDTree instead. (The only difference, I believe, is implementation... the behavior and interface is the same.)

[unutbu]

Thanks for the correction, @askewchan. cKDTree should be faster.

[Kitumijasi]

O.k now if I want to make your query for a lot or points how could I store the found nearest points with there query point? So in your example something like: (1.5 : 1 2) (1.6: 3 4) Like having an Index, dictionaries or tuple or something like that?

[unutbu]

I added an example showing how to perform the query for an array of points.