NearestCentroid classifier cannot handle data that is always exactly zero

Describe the bug

The NearestCentroid classifier cannot handle data that is always exactly zero in combination with using the shrink_threshold.

Steps/Code to Reproduce

import sklearn
from sklearn.neighbors import NearestCentroid

sklearn.show_versions()

X = [(0, 0),
     (0, 0),
     (0, 0),
     (0, 0),
     (0, 0),
     (0, 0),
     (0, 0),
     (0, 0),
     (0, 0),
     (0, 0)]

y = [0, 0, 1, 0, 0, 0, 1, 0, 1, 0]

clf = NearestCentroid(shrink_threshold=0.1)
clf.fit(X, y)
clf.predict(X)

Expected Results

Either no error is thrown and the data is handled correctly or a ValueError that specifies the concrete problem, i.e., that all feature values are the same.

Actual Results

C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\neighbors\nearest_centroid.py:159: RuntimeWarning: invalid value encountered in true_divide
  deviation = ((self.centroids_ - dataset_centroid_) / ms)
C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\neighbors\nearest_centroid.py:162: RuntimeWarning: invalid value encountered in sign
  signs = np.sign(deviation)
Traceback (most recent call last):
  File "C:/Users/sherbold/PycharmProjects/icb/tmp.py", line 21, in <module>
    clf.predict(X)
  File "C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\neighbors\nearest_centroid.py", line 194, in predict
    X, self.centroids_, metric=self.metric).argmin(axis=1)]
  File "C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\metrics\pairwise.py", line 1588, in pairwise_distances
    return _parallel_pairwise(X, Y, func, n_jobs, **kwds)
  File "C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\metrics\pairwise.py", line 1206, in _parallel_pairwise
    return func(X, Y, **kwds)
  File "C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\metrics\pairwise.py", line 232, in euclidean_distances
    X, Y = check_pairwise_arrays(X, Y)
  File "C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\metrics\pairwise.py", line 114, in check_pairwise_arrays
    estimator=estimator)
  File "C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\utils\validation.py", line 542, in check_array
    allow_nan=force_all_finite == 'allow-nan')
  File "C:\Users\sherbold\AppData\Local\Programs\Python\Python37\lib\site-packages\sklearn\utils\validation.py", line 56, in _assert_all_finite
    raise ValueError(msg_err.format(type_err, X.dtype))
ValueError: Input contains NaN, infinity or a value too large for dtype('float64').

Versions

System: python: 3.7.3 (v3.7.3:ef4ec6ed12, Mar 25 2019, 22:22:05) [MSC v.1916 64 bit (AMD64)] executable: C:\Users\sherbold\AppData\Local\Programs\Python\Python37\python.exe machine: Windows-10-10.0.19041-SP0

Python deps: pip: 19.0.3 setuptools: 42.0.1 sklearn: 0.21.3 numpy: 1.17.4 scipy: 1.3.2 Cython: None pandas: 0.25.3

[glemaitre]

@rushabh-v It seems that @Trevor-Waite already took the issue. However, there are plenty of other issues if you want to help.

[cmarmo]

Closed in #18370.