which estimators are those?

+1 to change the default in OPTICS (without deprecation cycle), especially considering that our euclidean is not robust.

which estimators are those?

from sklearn.utils.testing import all_estimators, ignore_warnings

for name, estimator in all_estimators():
    with ignore_warnings():
        params = estimator().get_params()

    keys = ['p', 'metric']

    if any(key in params for key in keys):
        msg = name + '('
        for key in keys:
            if key in params:
                msg += '%s=%r, ' % (key, params[key])
        msg = msg[:-2] + ')'
        print(msg)

# Results
DBSCAN(p=None, metric='euclidean')
KNeighborsClassifier(p=2, metric='minkowski')
KNeighborsRegressor(p=2, metric='minkowski')
KernelDensity(metric='euclidean')
LocalOutlierFactor(p=2, metric='minkowski')
MDS(metric=True)
NearestCentroid(metric='euclidean')
NearestNeighbors(p=2, metric='minkowski')
OPTICS(p=2, metric='euclidean')
RadiusNeighborsClassifier(p=2, metric='minkowski')
RadiusNeighborsRegressor(p=2, metric='minkowski')
TSNE(metric='euclidean')

So we have:

• DBSCAN. Interestingly, the function uses different defaults: dbscan(p=2, metric='minkowski'). we should probably fix this.
• OPTICS ([MRG] MNT Change default metric in OPTICS #12439)
• TSNE if we want to add parameter p ([MRG] Add distance metric_params argument to TSNE constructor #12387).
• KernelDensity if we want to add parameter p.
• MDS is not concerned.
• other estimators already have metric='minkowski' as default.

Hmmm.... @qinhanmin2014 has implied that this isn't the full story. Where sklearn.metrics.pairwise is used, unlike sklearn.neighbors, the implementation of minkowski(p=2) is not the same as the the implementation of euclidean.

Should pairwise_distances be special-casing the minkowski(p=2) case as equivalent to euclidean (and similar for manhattan)? Perhaps we should only do this after we've solved open issues with the precision of euclidean_distances.

I'll try to do this!

Should pairwise_distances be special-casing the minkowski(p=2) case as equivalent to euclidean (and similar for manhattan)? Perhaps we should only do this after we've solved open issues with the precision of euclidean_distances.

Yes, the solution proposed by @jnothman in #12601 (review) would be most elegant, but we need to come up with a solution to Euclidean distance accuracy first.

This is available for contributors to attempt, but it is not trivial.