dbscan float precision

[jurasofish]

Description

Incorrect clustering results when using dbscan clustering with brute algorithm and large values.
See the below code snippet - when the data type is changed to float64 or the algorithm is changed to ball_tree the correct clustering results are obtained.
For context, the large values are geographic coordinates.
I suspect this is because of the use of squared euclidean distance in the brute algorithm, which is outside the range where float32 can provide adequate precision:

scikit-learn/sklearn/neighbors/base.py

Line 699 in 7b136e9

# for efficiency, use squared euclidean distances

Perhaps it would be appropriate to warn if epsilon is so small compared to the values being clustered that it will cause issues with precision.

Steps/Code to Reproduce

import numpy as np
from sklearn.cluster import DBSCAN
from scipy.spatial import distance_matrix

import platform; print(platform.platform())
import sys; print("Python", sys.version)
import numpy; print("NumPy", numpy.__version__)
import scipy; print("SciPy", scipy.__version__)
import sklearn; print("Scikit-Learn", sklearn.__version__)

xy = np.array([[400000, 400000],
               [400000, 400000+1],
               [400000, 400000+5]
               ], dtype=np.float32)

print(distance_matrix(xy, xy))

print('incorrect', DBSCAN(eps=2, min_samples=1, algorithm='brute'
                          ).fit(xy.astype(np.float32)).labels_)
print('correct  ', DBSCAN(eps=2, min_samples=1, algorithm='brute'
                        ).fit(xy.astype(np.float64)).labels_)
print('correct  ', DBSCAN(eps=2, min_samples=1, algorithm='ball_tree'
                          ).fit(xy.astype(np.float32)).labels_)

Results

Windows-10-10.0.17134-SP0
Python 3.7.2 (default, Feb 21 2019, 17:35:59) [MSC v.1915 64 bit (AMD64)]
NumPy 1.16.1
SciPy 1.2.1
Scikit-Learn 0.20.3
[[0. 1. 5.]
 [1. 0. 4.]
 [5. 4. 0.]]
incorrect [0 1 0]
correct   [0 0 1]
correct   [0 0 1]

[jnothman]

Duplicate of #9354. Comment there?