kd树和寻找k近邻算法具体流程就不赘述了，这个链接写的很好懂 https://zhuanlan.zhihu.com/p/23966698
按照链接里的算法写了k近邻的python实现
from math import sqrt
class KDnode:
def __init__(self, data, left, right, split):
self.left = left
self.right = right
self.split = split
self.data = data
class KDtree:
def __init__(self,data):
self.k = len(data[0])
def CreatKD(split, data_set):
if not data_set:
return None
data_set.sort(key=lambda x: x[split])
flag = len(data_set)//2
new_split = (split+1) % self.k
return KDnode(data_set[flag], CreatKD(new_split,data_set[:flag]), CreatKD(new_split, data_set[flag+1:]), split)
self.root = CreatKD(0, data)
def nearest(tree, point, k):
L = []
def dis(x,p): #x是当前节点，p是目标节点
if len(L)<k:
d = sqrt(sum((x1-x2)**2 for x1, x2 in zip(x, p)))
L.append([x,d])
return
else:
d = sqrt(sum((x1 - x2) ** 2 for x1, x2 in zip(x, p)))
L.sort(key=lambda a: a[1])
if(L[-1][1] > d):
L.pop()
L.append([x, d])
return
def travel(kd_node):
if kd_node is None:
return
s = kd_node.split
if kd_node.data[s] > point[s]:
nearnode = kd_node.left
furthnode = kd_node.right
else:
nearnode = kd_node.right
furthnode = kd_node.left
travel(nearnode)
dis(kd_node.data, point)
dis1 = abs(kd_node.data[s] - point[s])
dis2 = sqrt(sum((x1 - x2) ** 2 for x1, x2 in zip(kd_node.data, point))) #最长距离
if len(L) < k or dis1 < dis2:
travel(furthnode)
else:
return
travel(tree.root)
return L
# data = [[2,3],[5,4],[9,6],[4,7],[8,1],[7,2]]
# kd = KDtree(data)
# ret = nearest(kd, [3,4.5], 2)
# print(ret)
from time import clock
from random import random
# 产生一个k维随机向量，每维分量值在0~1之间
def random_point(k):
return [random() for _ in range(k)]
# 产生n个k维随机向量
def random_points(k, n):
return [random_point(k) for _ in range(n)]
N = 400000
t0 = clock()
kd2 = KDtree(random_points(3, N)) # 构建包含四十万个3维空间样本点的kd树
t1= clock()
print("time: ", t1-t0, "s")
ret2 = nearest(kd2, [0.1,0.5,0.8], 2) # 四十万个样本点中寻找离目标最近的点
t2 = clock()
print("time: ", t2-t1, "s")
print(ret2)运行结果如下：
