代码行数230，由于每次执行代码选取的训练集不同，所以每次执行得到的正确率也不同，最好的情况是正确率达到83%。
特征值离散化的思路：
既然最终的分类是分成三种，那我猜测每个特征的取值也可以分成三个区间，那也就是求两个分割值。求分割值用双层for循环找使得信息熵最小的下标i和j。
代码整体思路:
1 . 先处理数据，shuffle函数随机抽取80%样本做训练集。
2 . 特征值离散化
3 . 用信息熵来递归地构造树
4 . 用构造好的树来判断剩下20%的测试集，求算法做分类的正确率
# coding: utf-8
# In[1]:
from sklearn import datasets
import math
import numpy as np
# In[69]:
def getInformationEntropy(arr,leng):
#print("length = ",leng)
return -(arr[0]/leng*math.log(arr[0]/leng if arr[0]>0 else 1)+ arr[1]/leng*math.log(arr[1]/leng if arr[1]>0 else 1)+ arr[2]/leng*math.log(arr[2]/leng if arr[2]>0 else 1))
#informationEntropy = getInformationEntropy(num,length)
#print(informationEntropy)
# In[105]:
#离散化特征一的值
def discretization(index):
feature1 = np.array([iris.data[:,index],iris.target]).T
feature1 = feature1[feature1[:,0].argsort()]
counter1 = np.array([0,0,0])
counter2 = np.array([0,0,0])
resEntropy = 100000
for i in range(len(feature1[:,0])):
counter1[int(feature1[i,1])] = counter1[int(feature1[i,1])] + 1
counter2 = np.copy(counter1)
for j in range(i+1,len(feature1[:,0])):
counter2[int(feature1[j,1])] = counter2[int(feature1[j,1])] + 1
#print(i,j,counter1,counter2)
#贪心算法求最优的切割点
if i != j and j != len(feature1[:,0])-1:
#print(counter1,i+1,counter2-counter1,j-i,np.array(num)-counter2,length-j-1)
sum = (i+1)*getInformationEntropy(counter1,i+1) + (j-i)*getInformationEntropy(counter2-counter1,j-i) + (length-j-1)*getInformationEntropy(np.array(num)-counter2,length-j-1)
if sum < resEntropy:
resEntropy = sum
res = np.array([i,j])
res_value = [feature1[res[0],0],feature1[res[1],0]]
print(res,resEntropy,res_value)
return res_value
# In[122]:
#求合适的分割值
def getRazors():
a = []
for i in range(len(iris.feature_names)):
print(i)
a.append(discretization(i))
return np.array(a)
# In[326]:
#随机抽取80%的训练集和20%的测试集
def divideData():
completeData = np.c_[iris.data,iris.target.T]
np.random.shuffle(completeData)
trainData = completeData[range(int(length*0.8)),:]
testData = completeData[range(int(length*0.8),length),:]
return [trainData,testData]
# In[213]:
def getEntropy(counter):
res = 0
denominator = np.sum(counter)
if denominator == 0:
return 0
for value in counter:
if value == 0:
continue
res += value/denominator * math.log(value/denominator if value>0 and denominator>0 else 1)
return -res
# In[262]:
def findMaxIndex(dataSet):
maxIndex = 0
maxValue = -1
for index,value in enumerate(dataSet):
if value>maxValue:
maxIndex = index
maxValue = value
return maxIndex
# In[308]:
def recursion(featureSet,dataSet,counterSet):
#print("函数开始，剩余特征：",featureSet," 剩余结果长度：",len(dataSet))
if(counterSet[0]==0 and counterSet[1]==0 and counterSet[2]!=0):
return iris.target_names[2]
if(counterSet[0]!=0 and counterSet[1]==0 and counterSet[2]==0):
return iris.target_names[0]
if(counterSet[0]==0 and counterSet[1]!=0 and counterSet[2]==0):
return iris.target_names[1]
if len(featureSet) == 0:
return iris.target_names[findMaxIndex(counterSet)]
if len(dataSet) == 0:
return []
res = 1000
final = 0
#print("剩余特征数目", len(featureSet))
for feature in featureSet:
i = razors[feature][0]
j = razors[feature][1]
#print("i = ",i," j = ",j)
set1 = []
set2 = []
set3 = []
counter1 = [0,0,0]
counter2 = [0,0,0]
counter3 = [0,0,0]
for data in dataSet:
index = int(data[-1])
#print("data ",data," index ",index)
if data[feature]< i :
set1.append(data)
counter1[index] = counter1[index]+1
elif data[feature] >= i and data[feature] <=j:
set2.append(data)
counter2[index] = counter2[index]+1
else:
set3.append(data)
counter3[index] = counter3[index]+1
a =( len(set1)*getEntropy(counter1) + len(set2)*getEntropy(counter2) + len(set3)*getEntropy(counter3) )/ len(dataSet)
#print("特征编号：",feature,"选取该特征得到的信息熵:",a)
if a<res :
res = a
final = feature
#返回被选中的特征的下标
#sequence.append(final)
#print("最终在本节点上选取的特征编号是:",final)
featureSet.remove(final)
child = [0,0,0,0]
child[0] = final
child[1] = recursion(featureSet,set1,counter1)
child[2] = recursion(featureSet,set2,counter2)
child[3] = recursion(featureSet,set3,counter3)
return child
# In[322]:
def judge(data,tree):
root = "unknow"
while(len(tree)>0):
if isinstance(tree,str) and tree in iris.target_names:
return tree
root = tree[0]
if(isinstance(root,str)):
return root
if isinstance(root,int):
if data[root]<razors[root][0] and tree[1] != [] :
tree = tree[1]
elif tree[2] != [] and (tree[1]==[] or (data[root]>=razors[root][0] and data[root]<=razors[root][1])):
tree = tree[2]
else :
tree = tree[3]
return root
# In[327]:
if __name__ == '__main__':
iris = datasets.load_iris()
num = [0,0,0]
for row in iris.data:
num[int(row[-1])] = num[int(row[-1])] + 1
length = len(iris.target)
[trainData,testData] = divideData()
razors = getRazors()
tree = recursion(list(range(len(iris.feature_names))), trainData,[np.sum(trainData[:,-1]==0), np.sum(trainData[:,-1]==1),np.sum(trainData[:,-1]==2)])
print("本次选取的训练集构建出的树： ",tree)
index = 0
right = 0
for data in testData:
result = judge(testData[index],tree)
truth = iris.target_names[int(testData[index][-1])]
print("result is ",result ," truth is ",truth)
index = index + 1
if result == truth:
right = right + 1
print("正确率 ： ",right/index)
