Decision Tree 及实现

cathleenhaenke 计算机知识 394 次浏览 没有评论

本文基于python逐步实现Decision Tree(决策树),分为以下几个步骤:

  • 加载数据集
  • 熵的计算
  • 根据最佳分割feature进行数据分割
  • 根据最大信息增益选择最佳分割feature
  • 递归构建决策树
  • 样本分类

关于决策树的理论方面本文几乎不讲,详情请google keywords:“决策树 信息增益  熵”

将分别体现于代码。

本文只建一个.py文件,所有代码都在这个py里



1.加载数据集

我们选用UCI经典Iris为例

Brief of IRIS:

Data Set Characteristics:  

Multivariate

Number of Instances:

150

Area:

Life

Attribute Characteristics:

Real

Number of Attributes:

4

Date Donated

1988-07-01

Associated Tasks:

Classification

Missing Values?

No

Number of Web Hits:

533125


Code:

from numpy import * #load "iris.data" to workspace traindata = loadtxt("D:/ZJU_Projects/machine learning/ML_Action/Dataset/Iris.data",delimiter = ',',usecols = (0,1,2,3),dtype = float) trainlabel = loadtxt("D:/ZJU_Projects/machine learning/ML_Action/Dataset/Iris.data",delimiter = ',',usecols = (range(4,5)),dtype = str) feaname = ["#0","#1","#2","#3"] # feature names of the 4 attributes (features)

Result

Decision Tree 及实现           Decision Tree 及实现

左图为实际数据集,四个离散型feature,一个label表示类别(有Iris-setosa, Iris-versicolor,Iris-virginica 三个类)




2. 熵的计算

entropy是香农提出来的(信息论大牛),定义见wiki

注意这里的entropy是H(C|X=xi)而非H(C|X), H(C|X)的计算见第下一个点,还要乘以概率加和

Code:

from math import log def calentropy(label):     n = label.size # the number of samples     #print n     count = {} #create dictionary "count"     for curlabel in label:         if curlabel not in count.keys():             count[curlabel] = 0         count[curlabel] += 1     entropy = 0     #print count     for key in count:         pxi = float(count[key])/n #notice transfering to float first         entropy -= pxi*log(pxi,2)     return entropy  #testcode: #x = calentropy(trainlabel)


Result:

Decision Tree 及实现






3. 根据最佳分割feature进行数据分割

假定我们已经得到了最佳分割feature,在这里进行分割(最佳feature为splitfea_idx)

第二个函数idx2data是根据splitdata得到的分割数据的两个index集合返回datal (samples less than pivot), datag(samples greater than pivot), labell, labelg。 这里我们根据所选特征的平均值作为pivot

#split the dataset according to label "splitfea_idx" def splitdata(oridata,splitfea_idx):     arg = args[splitfea_idx] #get the average over all dimensions     idx_less = [] #create new list including data with feature less than pivot     idx_greater = [] #includes entries with feature greater than pivot     n = len(oridata)     for idx in range(n):         d = oridata[idx]         if d[splitfea_idx] < arg:             #add the newentry into newdata_less set             idx_less.append(idx)         else:             idx_greater.append(idx)     return idx_less,idx_greater  #testcode:2 #idx_less,idx_greater = splitdata(traindata,2)   #give the data and labels according to index def idx2data(oridata,label,splitidx,fea_idx):     idxl = splitidx[0] #split_less_indices     idxg = splitidx[1] #split_greater_indices     datal = []     datag = []     labell = []     labelg = []     for i in idxl:         datal.append(append(oridata[i][:fea_idx],oridata[i][fea_idx+1:]))     for i in idxg:         datag.append(append(oridata[i][:fea_idx],oridata[i][fea_idx+1:]))     labell = label[idxl]     labelg = label[idxg]     return datal,datag,labell,labelg

这里args是参数,决定分裂节点的阈值(每个参数对应一个feature,大于该值分到>branch,小于该值分到<branch),我们可以定义如下:

args = mean(traindata,axis = 0)

测试:按特征2进行分类,得到的less和greater set of indices分别为:


Decision Tree 及实现

也就是按args[2]进行样本集分割,<和>args[2]的branch分别有57和93个样本。




4. 根据最大信息增益选择最佳分割feature

信息增益为代码中的info_gain, 注释中是熵的计算

#select the best branch to split def choosebest_splitnode(oridata,label):     n_fea = len(oridata[0])     n = len(label)     base_entropy = calentropy(label)     best_gain = -1     for fea_i in range(n_fea): #calculate entropy under each splitting feature         cur_entropy = 0         idxset_less,idxset_greater = splitdata(oridata,fea_i)         prob_less = float(len(idxset_less))/n         prob_greater = float(len(idxset_greater))/n                  #entropy(value|X) = /sum{p(xi)*entropy(value|X=xi)}         cur_entropy += prob_less*calentropy(label[idxset_less])         cur_entropy += prob_greater * calentropy(label[idxset_greater])                  info_gain = base_entropy - cur_entropy #notice gain is before minus after         if(info_gain>best_gain):             best_gain = info_gain             best_idx = fea_i     return best_idx    #testcode: #x = choosebest_splitnode(traindata,trainlabel) 

这里的测试针对所有数据,分裂一次选择哪个特征呢?

Decision Tree 及实现





5. 递归构建决策树

详见code注释,buildtree递归地构建树。

递归终止条件:

①该branch内没有样本(subset为空) or

②分割出的所有样本属于同一类 or 

③由于每次分割消耗一个feature,当没有feature的时候停止递归,返回当前样本集中大多数sample的label


#create the decision tree based on information gain def buildtree(oridata, label):     if label.size==0: #if no samples belong to this branch         return "NULL"     listlabel = label.tolist()     #stop when all samples in this subset belongs to one class     if listlabel.count(label[0])==label.size:         return label[0]              #return the majority of samples' label in this subset if no extra features avaliable     if len(feanamecopy)==0:         cnt = {}         for cur_l in label:             if cur_l not in cnt.keys():                 cnt[cur_l] = 0             cnt[cur_l] += 1         maxx = -1          for keys in cnt:             if maxx < cnt[keys]:                 maxx = cnt[keys]                 maxkey = keys         return maxkey          bestsplit_fea = choosebest_splitnode(oridata,label) #get the best splitting feature     print bestsplit_fea,len(oridata[0])     cur_feaname = feanamecopy[bestsplit_fea] # add the feature name to dictionary     print cur_feaname     nodedict = {cur_feaname:{}}      del(feanamecopy[bestsplit_fea]) #delete current feature from feaname     split_idx = splitdata(oridata,bestsplit_fea) #split_idx: the split index for both less and greater     data_less,data_greater,label_less,label_greater = idx2data(oridata,label,split_idx,bestsplit_fea)          #build the tree recursively, the left and right tree are the "<" and ">" branch, respectively     nodedict[cur_feaname]["<"] = buildtree(data_less,label_less)     nodedict[cur_feaname][">"] = buildtree(data_greater,label_greater)     return nodedict      #testcode: #mytree = buildtree(traindata,trainlabel) #print mytree

Result:

Decision Tree 及实现

mytree就是我们的结果,#1表示当前使用第一个feature做分割,'<‘和’>’分别对应less 和 greater的数据。





6. 样本分类

根据构建出的mytree进行分类,递归走分支

#classify a new sample def classify(mytree,testdata):     if type(mytree).__name__ != 'dict':         return mytree     fea_name = mytree.keys()[0] #get the name of first feature     fea_idx = feaname.index(fea_name) #the index of feature 'fea_name'     val = testdata[fea_idx]     nextbranch = mytree[fea_name]          #judge the current value > or < the pivot (average)     if val>args[fea_idx]:         nextbranch = nextbranch[">"]     else:         nextbranch = nextbranch["<"]     return classify(nextbranch,testdata)  #testcode tt = traindata[0] x = classify(mytree,tt) print x

Decision Tree 及实现


为了验证代码准确性,我们换一下args参数,把它们都设成0(很小)

args = [0,0,0,0]

建树和分类的结果如下:

Decision Tree 及实现

可见没有小于pivot(0)的项,于是dict中每个<的key对应的value都为空。


本文中全部代码下载:决策树python实现

Reference: Machine Learning in Action



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