决策树分类鸢尾花数据集python实现

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)

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