最近邻搜索 4D 空间 python 快速 - 矢量化

Question

对于 X 中的每个观察值（有 20 个），我想获得 k(3) 个最近的邻居。 如何让它快速支持多达 3 到 400 万行？ 是否可以加快循环遍历元素的速度？也许通过 numpy、numba 或某种矢量化？

python 中的一个简单循环：

import numpy as np
from sklearn.neighbors import KDTree

n_points = 20
d_dimensions = 4
k_neighbours = 3

rng = np.random.RandomState(0)
X = rng.random_sample((n_points, d_dimensions))
print(X)
tree = KDTree(X, leaf_size=2, metric='euclidean')

for element in X:
    print('********')
    print(element)

# when simply using the first row
#element = X[:1]
#print(element)

    # potential optimization: query_radius https://scikit-learn.org/stable/modules/generated/sklearn.neighbors.KDTree.html#sklearn.neighbors.KDTree.query_radius
    dist, ind = tree.query([element], k=k_neighbours, return_distance=True, dualtree=False, breadth_first=False, sort_results=True)

    # indices of 3 closest neighbors
    print(ind)
    #[[0 9 1]] !! includes self (element that was searched for)
    print(dist)  # distances to 3 closest neighbors
    #[[0.         0.38559188 0.40997835]] !! includes self (element that was searched for)

    # actual returned elements for index:
    print(X[ind])

    ## after removing self
    print(X[ind][0][1:])

最佳输出是具有以下结构的 pandas.DataFrame：

lat_1,long_1,lat_2,long_2,neighbours_list
0.5488135,0.71518937,0.60276338,0.54488318, [[0.61209572 0.616934   0.94374808 0.6818203 ][0.4236548  0.64589411 0.43758721 0.891773]

编辑

目前，我有一个基于 pandas 的实现：

df = df.dropna() # there are sometimes only parts of the tuple (either left or right) defined
X = df[['lat1', 'long1', 'lat2', 'long2']]
tree = KDTree(X, leaf_size=4, metric='euclidean')

k_neighbours = 3
def neighbors_as_list(row, index, complete_list):
    dist, ind = index.query([[row['lat1'], row['long1'], row['lat2'], row['long2']]], k=k_neighbours, return_distance=True, dualtree=False, breadth_first=False, sort_results=True)
    return complete_list.values[ind][0][1:]    
df['neighbors'] = df.apply(neighbors_as_list, index=tree, complete_list=X, axis=1)
df.head()

但这很慢。

编辑 2

当然，这是 pandas 版本：

import numpy as np
import pandas as pd

from sklearn.neighbors import KDTree
from scipy.spatial import cKDTree

rng = np.random.RandomState(0)
#n_points = 4_000_000
n_points = 20
d_dimensions = 4
k_neighbours = 3

X = rng.random_sample((n_points, d_dimensions))
X


df = pd.DataFrame(X)
df = df.reset_index(drop=False)
df.columns = ['id_str', 'lat_1', 'long_1', 'lat_2', 'long_2']
df.id_str = df.id_str.astype(object)
display(df.head())

tree = cKDTree(df[['lat_1', 'long_1', 'lat_2', 'long_2']])
dist,ind=tree.query(X, k=k_neighbours,n_jobs=-1)

display(dist)
print(df[['lat_1', 'long_1', 'lat_2', 'long_2']].shape)
print(X[ind_out].shape)
X[ind_out]

# fails with
# AssertionError: Shape of new values must be compatible with manager shape
df['neighbors'] = X[ind_out]
df

但它失败了，因为我无法重新分配结果。

Answer 1

你可以使用 scipy 的 cKdtree。

示例

rng = np.random.RandomState(0)
n_points = 4_000_000
d_dimensions = 4
k_neighbours = 3

X = rng.random_sample((n_points, d_dimensions))

tree = cKDTree(X)

#%timeit tree = cKDTree(X)
#3.74 s ± 29.6 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

#%%timeit
_,ind=tree.query(X, k=k_neighbours,n_jobs=-1)
#shape=(4000000, 2)
ind_out=ind[:,1:]

#shape=(4000000, 2, 4)
coords_out=X[ind_out].shape
#7.13 s ± 87.1 ms per loop (mean ± std. dev. of 7 runs, 1 loop each)

这种规模的问题大约 11 秒是相当不错的。