k近邻算法是机器学习中原理最简单的算法之一,其思想为:给定测试样本,计算出距离其最近的k个训练样本,将这k个样本中出现类别最多的标记作为该测试样本的预测标记。
k近邻算法虽然原理简单,但是其泛华错误率却不超过贝叶斯最有分类器错误率的两倍。所以实际应用中,k近邻算法是一个“性价比”很高的分类工具。
基于欧式距离,用Python3.5实现kNN算法:
主程序:
from numpy import*
import operator
def myED(testdata,traindata):
""" 计算欧式距离,要求测试样本和训练样本以array([ [],[],...[] ])的形式组织,
每行表示一个样本,一列表示一个属性"""
size_train=traindata.shape[0] # 训练样本量大小
size_test=testdata.shape[0] # 测试样本大小
XX=traindata**2
sumXX=XX.sum(axis=1) # 行平方和
YY=testdata**2
sumYY=YY.sum(axis=1) # 行平方和
Xpw2_plus_Ypw2=tile(mat(sumXX).T,[1,size_test])+\
tile(mat(sumYY),[size_train,1])
EDsq=Xpw2_plus_Ypw2-2*(mat(traindata)*mat(testdata).T) # 欧式距离平方
distances=array(EDsq)**0.5 #欧式距离
return distances
def mykNN(testdata,traindata,labels,k):
""" kNN算法主函数,labels组织成列表形式 """
size_test=testdata.shape[0]
D=myED(testdata,traindata)
Dsortindex=D.argsort(axis=0) # 距离排序,提取序号
nearest_k=Dsortindex[0:k,:] # 提取最近k个距离的样本序号
label_nearest_k=array(labels)[nearest_k] # 提取最近k个距离样本的标签
label_test=[]
if k==1:
label_test=label_nearest_k
else:
for smp in range(size_test):
classcount={}
labelset=set(label_nearest_k[:,smp]) # k个近邻样本的标签集合
for label in labelset:
classcount[label]=list(label_nearest_k[:,smp]).count(label)
# 遍历k个近邻样本的标签,并计数,并以字典保存标签和计数结果
sortedclasscount=sorted(classcount.items(),\
key=operator.itemgetter(1),reverse=True) # 按照计数结果排序
label_test.append(sortedclasscount[0][0]) # 提取出现最多的标签
return label_test,D
示例:
# 以下示例数据摘自周志华《机器学习》P202表9.1
labels=[1,1,1,1,1,1,1,1,0,0,0,0,0,0,0,0,0]
traindata=array([[0.6970,0.4600],[0.7740,0.3760],[0.6340,0.2640],\
[0.6080,0.3180],[0.5560,0.2150],[0.4030,0.2370],[0.4810,0.1490],\
[0.4370,0.2110],[0.6660,0.0910],[0.2430,0.2670],[0.2450,0.0570],\
[0.3430,0.0990],[0.6390,0.1610],[0.6570,0.1980],[0.3600,0.3700],\
[0.5930,0.0420],[0.7190,0.1030]])
testdata=array([[0.3590,0.1880],[0.3390,0.2410],[0.2820,0.2570],\
[0.7480,0.2320],[0.7140,0.3460],[0.4830,0.3120],[0.4780,0.4370],\
[0.5250,0.3690],[0.7510,0.4890],[0.5320,0.4720],[0.4730,0.3760],\
[0.7250,0.4450],[0.4460,0.4590]])
k=5
label_test,distances=mykNN(testdata,traindata,labels,k)
print('\n')
print(label_test)
示例结果:
>>[1, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1]