I am trying to run Density-Based Spatial Clustering (DBSCAN) on a Point Cloud dataset which is a series of points with x,y,z coordinates. One of the parameters in min distance. How do I find the minimal distance between a point and another in space in Python? Many thanks!

Data Sample:

First you can write a function that computes the euclidian distance between two points represented as numpy arrays :

import numpy as np

distance = lambda p1, p2: np.sqrt(np.sum((p1 - p2) ** 2, axis=0))

I can't think of anything better than the naive O(n²) to find the minimum distance :

import itertools

def min_distance(cloud):
  pairs = itertools.combinations(cloud, 2)
  return np.min(map(lambda pair: distance(*pair), pairs))

Finally, you just need to get the points from your file, I will assume that it looks like this :

cloud.csv

x, y, z
1.2, 3.4, 2.55
2.77, 7.34, 23.4
5.66, 64.3, 4.33

def get_points(filename):
  with open(filename, 'r') as file:
    rows = np.genfromtxt(file, delimiter=',', skip_header=True)
  return rows

Final code

import itertools
import numpy as np

distance = lambda p1, p2: np.sqrt(np.sum((p1 - p2) ** 2, axis=0))


def min_distance(cloud):
  pairs = itertools.combinations(cloud, 2)
  return np.min(map(lambda pair: distance(*pair), pairs))


def get_points(filename):
  with open(filename, 'r') as file:
    rows = np.genfromtxt(file, delimiter=',', skip_header=True)
  return rows


filename = 'cloud.csv'
cloud = get_points(filename)
min_dist = min_distance(cloud)

print(min_dist)

Output

21.277006368378046

Edit

As Amiga500 points out, it is possible to use scipy.spatial.distance. We can then rewrite min_distance as follows:

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

min_distance = lambda cloud: np.min(pdist(cloud))