Add callable metric support for KDTree algorithm

Description

Related Issue: https://github.com/scikit-learn/scikit-learn/issues/10386 Currently, a callable metric for the KDTree is not supported. For example, when using NearestNeighbors as an interface for neighbors algorithm:

Steps/Code to Reproduce

def heom_metric(x, y):
    # metric function
    # E.g Heterogeneous Euclidian-Overlap Metric
    pass

nbrs_kd = NearestNeighbors(algorithm='kd_tree',
    metric=heom_metric)

nbrs_ball = NearestNeighbors(algorithm='ball_tree',
    metric=heom_metric)

Expected Results

Code runs correctly without any ValueError thrown

Actual Results

nbrs_kd will throw a ValueError that a callable metric is not supported. It would be helpful to make the API consistent and add callable metric support to KDTree as well. At the moment it is a bit misleading as metrics are not consistent among different Nearest Neighbors Algorithms.

[adrinjalali]

That’ll add quite a bit of complexity to the existing code. If somebody ends up submittig a PR which looks like nice maintainable code and doesn’t add a time penalty to the existing one, I’m happy to review.

[VolodyaCO]

There are some applications where a custom metric is needed (even if it is slower). I recently wanted to use cKDTree (with periodic boundary conditions) with a custom metric for molecular dynamics purposes, but it was impossible. @amueller will this feature request be reconsidered?