DrBwts - 1 year ago 102

Python Question

I have an array of 1000 random 3D points & I am interested in the closest 10 points to any given point. In essence the same as this post.

I checked the 2 solutions offered by J.F. Sebastian, namely a brute force approach & a KD Tree approach.

Although both give me the same indices for the closest points, they give different results for the distances

`import numpy as np`

from scipy.spatial import KDTree

a = 100 * np.random.rand(1000,3)

point = a[np.random.randint(0, 1001)] # point chosen at random

# KD Tree

tree = KDTree(a, leafsize=a.shape[0]+1)

dist_kd, ndx_kd = tree.query([point], k=10)

# Brute force

distances = ((a-point)**2).sum(axis=1) # compute distances

ndx = distances.argsort() # indirect sort

ndx_brt = ndx[:10]

dist_brt = distances[ndx[:10]]

# Output

print 'KD Tree:'

print ndx_kd

print dist_kd

print 'Brute force:'

print ndx_brt

print dist_brt

My output,

KD Tree:

[[838 860 595 684 554 396 793 197 652 330]]

[[ 0. 3.00931208 8.30596471 9.47709122 10.98784209

11.39555636 11.89088764 12.01566931 12.551557 12.77700426]]

Brute force:

[838 860 595 684 554 396 793 197 652 330]

[ 0. 9.05595922 68.9890498 89.81525793 120.73267386

129.8587047 141.3932089 144.37630888 157.54158301 163.25183793]

So what is the issue here? Am I calculating the distance wrong?

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Answer Source

`KDTree`

algorithm is computing the nearest points based on the square-root of the same distance used by `Brute-force`

algorithm.

Basically KDtree uses: `sqrt(x^2+y^2+z^2)`

and Brute-force algorithm uses: `x^2+y^2+z^2`

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