[Bug] API normalized_mutual_info_score may violate Symmetry.

[Z712023]

Description

The output of api normalized_mutual_info_score may violate Symmetry, although the official documentation claims that
"This metric is furthermore symmetric: switching label_true with label_pred will return the same score value. "https://scikit-learn.org/stable/modules/generated/sklearn.metrics.normalized_mutual_info_score.html

Reproduce

1. Run the code as follows:

from sklearn.preprocessing import LabelEncoder
from sklearn.metrics.cluster import normalized_mutual_info_score

a = "guest"
b = "user"
c = "admin"

src = [a,c,b,b,c,a,c,a,c,c]
tar = [a,b,a,a,b,c,b,b,c,a]
test_nums = 100
for i in range(test_nums):
le = LabelEncoder()
src_list = list(set(src))
tar_list = list(set(tar))
fit_list = tar_list + src_list
le.fit(fit_list)
src_col = le.transform(src)
tar_col = le.transform(tar)
test1 = normalized_mutual_info_score(src_col, tar_col,average_method='geometric')
test2 = normalized_mutual_info_score(tar_col, src_col,average_method='geometric')
print(f"iter:{i}: test1:{test1} test2:{test2}")
print(src_col,tar_col)
print(tar_col,src_col)
assert test2==test1

2. I tried different choices for average_method, but the error was still there.

Expected behavior

Keep the Symmetry property of normalized mutual information. We may need to rewrite code by ourselves.

Context

• Operating System and version: Mac OS 12.5.1
• sdgx==0.1.4.dev0
• scikit-learn==1.3.2

[Z712023]

I traced back this problem and found that the difference is the out of sum at https://github.com/scikit-learn/scikit-learn/blob/3f89022fa04d293152f1d32fbc2a5bdaaf2df364/sklearn/metrics/cluster/_supervised.py#L900
I think the reason is the design of float in Python, so the output of normalized_mutual_info_score can be accurate within a certain precision.