Python语言描述KNN算法与Kd树 Python语言描述KNN算法与Kd树

from numpy import * 

# create a dataset which contains 4 samples with 2 classes 
def createDataSet(): 
  # create a matrix: each row as a sample 
  group = array([[1.0, 0.9], [1.0, 1.0], [0.1, 0.2], [0.0, 0.1]]) 
  labels = ['A', 'A', 'B', 'B'] # four samples and two classes 
  return group, labels
# classify using kNN (k Nearest Neighbors ) 
# Input:   newInput: 1 x N
#       dataSet: M x N (M samples N, features)
#       labels:  1 x M  
#       k: number of neighbors to use for comparison 
# Output:   the most popular class label  
def kNNClassify(newInput, dataSet, labels, k): 
  numSamples = dataSet.shape[0] # shape[0] stands for the num of row 
  ## step 1: calculate Euclidean distance 
  # tile(A, reps): Construct an array by repeating A reps times 
  # the following copy numSamples rows for dataSet 
  diff = tile(newInput, (numSamples, 1)) - dataSet # Subtract element-wise 
  squaredDiff = diff ** 2 # squared for the subtract 
  squaredDist = sum(squaredDiff, axis = 1) # sum is performed by row 
  distance = squaredDist ** 0.5 
  ## step 2: sort the distance 
  # argsort() returns the indices that would sort an array in a ascending order 
  sortedDistIndices = argsort(distance) 
  classCount = {} # define a dictionary (can be append element) 
  for i in xrange(k): 
    ## step 3: choose the min k distance 
    voteLabel = labels[sortedDistIndices[i]] 
    ## step 4: count the times labels occur 
    # when the key voteLabel is not in dictionary classCount, get() 
    # will return 0 
    classCount[voteLabel] = classCount.get(voteLabel, 0) + 1 
  ## step 5: the max voted class will return 
  maxCount = 0 
  for key, value in classCount.items(): 
    if value > maxCount: 
      maxCount = value 
      maxIndex = key 
  return maxIndex  
  if __name__== "__main__":  
  dataSet, labels = createDataSet() 
  testX = array([1.2, 1.0]) 
  k = 3 
  outputLabel = kNNClassify(testX, dataSet, labels, 3) 
  print "Your input is:", testX, "and classified to class: ", outputLabel 
  testX = array([0.1, 0.3]) 
  outputLabel = kNNClassify(testX, dataSet, labels, 3) 
  print "Your input is:", testX, "and classified to class: ", outputLabel

import numpy as np
import matplotlib.pyplot as plt
import cv2
# Feature set containing (x,y) values of 25 known/training data
trainData = np.random.randint(0,100,(25,2)).astype(np.float32)
# Labels each one either Red or Blue with numbers 0 and 1
responses = np.random.randint(0,2,(25,1)).astype(np.float32)
# Take Red families and plot them
red = trainData[responses.ravel()==0]
plt.scatter(red[:,0],red[:,1],80,'r','^')
# Take Blue families and plot them
blue = trainData[responses.ravel()==1]
plt.scatter(blue[:,0],blue[:,1],80,'b','s')
# Testing data
newcomer = np.random.randint(0,100,(1,2)).astype(np.float32)
plt.scatter(newcomer[:,0],newcomer[:,1],80,'g','o')
knn = cv2.KNearest()
knn.train(trainData,responses) # Trains the model
# Finds the neighbors and predicts responses for input vectors.
ret, results, neighbours ,dist = knn.find_nearest(newcomer, 3)
print "result: ", results,"\n"
print "neighbours: ", neighbours,"\n"
print "distance: ", dist
plt.show()

>>> 
result: [[ 0.]]
neighbours: [[ 0. 0. 0.]]
distance: [[ 65. 145. 178.]]

# -*- coding: utf-8 -*-
#from operator import itemgetter
import sys
reload(sys)
sys.setdefaultencoding('utf8')
# kd-tree每个结点中主要包含的数据结构如下 
class KdNode(object):
  def __init__(self, dom_elt, split, left, right):
    self.dom_elt = dom_elt # k维向量节点(k维空间中的一个样本点)
    self.split = split   # 整数（进行分割维度的序号）
    self.left = left    # 该结点分割超平面左子空间构成的kd-tree
    self.right = right   # 该结点分割超平面右子空间构成的kd-tree
class KdTree(object):
  def __init__(self, data):
    k = len(data[0]) # 数据维度
    
    def CreateNode(split, data_set): # 按第split维划分数据集exset创建KdNode
      if not data_set:  # 数据集为空
        return None
      # key参数的值为一个函数，此函数只有一个参数且返回一个值用来进行比较
      # operator模块提供的itemgetter函数用于获取对象的哪些维的数据，参数为需要获取的数据在对象中的序号
      #data_set.sort(key=itemgetter(split)) # 按要进行分割的那一维数据排序
      data_set.sort(key=lambda x: x[split])
      split_pos = len(data_set) // 2   # //为Python中的整数除法
      median = data_set[split_pos]    # 中位数分割点       
      split_next = (split + 1) % k    # cycle coordinates      
      # 递归的创建kd树
      return KdNode(median, split, 
             CreateNode(split_next, data_set[:split_pos]),   # 创建左子树
             CreateNode(split_next, data_set[split_pos + 1:])) # 创建右子树                
    self.root = CreateNode(0, data)     # 从第0维分量开始构建kd树,返回根节点
# KDTree的前序遍历
def preorder(root): 
  print root.dom_elt 
  if root.left:   # 节点不为空
    preorder(root.left) 
  if root.right: 
    preorder(root.right) 
if __name__ == "__main__":
  data = [[2,3],[5,4],[9,6],[4,7],[8,1],[7,2]]
  kd = KdTree(data)
  preorder(kd.root)

from math import sqrt
from collections import namedtuple
# 定义一个namedtuple,分别存放最近坐标点、最近距离和访问过的节点数
result = namedtuple("Result_tuple", "nearest_point nearest_dist nodes_visited") 
def find_nearest(tree, point):
  k = len(point) # 数据维度
  def travel(kd_node, target, max_dist):
    if kd_node is None:   
      return result([0] * k, float("inf"), 0) # python中用float("inf")和float("-inf")表示正负无穷 
    nodes_visited = 1    
    s = kd_node.split    # 进行分割的维度
    pivot = kd_node.dom_elt # 进行分割的“轴”    
    if target[s] <= pivot[s]:      # 如果目标点第s维小于分割轴的对应值(目标离左子树更近)
      nearer_node = kd_node.left   # 下一个访问节点为左子树根节点
      further_node = kd_node.right  # 同时记录下右子树
    else:                # 目标离右子树更近
      nearer_node = kd_node.right  # 下一个访问节点为右子树根节点
      further_node = kd_node.left 
    temp1 = travel(nearer_node, target, max_dist) # 进行遍历找到包含目标点的区域    
    nearest = temp1.nearest_point    # 以此叶结点作为“当前最近点”
    dist = temp1.nearest_dist      # 更新最近距离    
    nodes_visited += temp1.nodes_visited 
    if dist < max_dist:   
      max_dist = dist  # 最近点将在以目标点为球心，max_dist为半径的超球体内
    temp_dist = abs(pivot[s] - target[s])  # 第s维上目标点与分割超平面的距离
    if max_dist < temp_dist:        # 判断超球体是否与超平面相交
      return result(nearest, dist, nodes_visited) # 不相交则可以直接返回，不用继续判断 
    #---------------------------------------------------------------------- 
    # 计算目标点与分割点的欧氏距离 
    temp_dist = sqrt(sum((p1 - p2) ** 2 for p1, p2 in zip(pivot, target)))   
    if temp_dist < dist:     # 如果“更近”
      nearest = pivot     # 更新最近点
      dist = temp_dist     # 更新最近距离
      max_dist = dist     # 更新超球体半径
    
    # 检查另一个子结点对应的区域是否有更近的点
    temp2 = travel(further_node, target, max_dist) 
    nodes_visited += temp2.nodes_visited
    if temp2.nearest_dist < dist:    # 如果另一个子结点内存在更近距离
      nearest = temp2.nearest_point  # 更新最近点
      dist = temp2.nearest_dist    # 更新最近距离
    return result(nearest, dist, nodes_visited)
  return travel(tree.root, point, float("inf")) # 从根节点开始递归

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)]    
   if __name__ == "__main__":
  data = [[2,3],[5,4],[9,6],[4,7],[8,1],[7,2]] # samples
    kd = KdTree(data)
    ret = find_nearest(kd, [3,4.5])
  print ret
  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
  ret2 = find_nearest(kd2, [0.1,0.5,0.8])   # 四十万个样本点中寻找离目标最近的点
  t1 = clock()
  print "time: ",t1-t0, "s"
  print ret2