上一篇博客主要介绍了决策树的原理，这篇主要介绍他的实现，代码环境python 3.4，实现的是ID3算法，首先为了后面matplotlib的绘图方便，我把原来的中文数据集变成了英文。

原始数据集：

变化后的数据集在程序代码中体现，这就不截图了

构建决策树的代码如下：

#coding :utf-8'''2017.6.25 author :Erin function: "decesion tree" ID3 '''import numpy as npimport pandas as pdfrom math import logimport operator def load_data(): #data=np.array(data) data=[['teenager' ,'high', 'no' ,'same', 'no'], ['teenager', 'high', 'no', 'good', 'no'], ['middle_aged' ,'high', 'no', 'same', 'yes'], ['old_aged', 'middle', 'no' ,'same', 'yes'], ['old_aged', 'low', 'yes', 'same' ,'yes'], ['old_aged', 'low', 'yes', 'good', 'no'], ['middle_aged', 'low' ,'yes' ,'good', 'yes'], ['teenager' ,'middle' ,'no', 'same', 'no'], ['teenager', 'low' ,'yes' ,'same', 'yes'], ['old_aged' ,'middle', 'yes', 'same', 'yes'], ['teenager' ,'middle', 'yes', 'good', 'yes'], ['middle_aged' ,'middle', 'no', 'good', 'yes'], ['middle_aged', 'high', 'yes', 'same', 'yes'], ['old_aged', 'middle', 'no' ,'good' ,'no']] features=['age','input','student','level'] return data,features def cal_entropy(dataSet): ''' 输入data ,表示带最后标签列的数据集 计算给定数据集总的信息熵 {'是': 9, '否': 5} 0.9402859586706309 ''' numEntries = len(dataSet) labelCounts = {} for featVec in dataSet: label = featVec[-1] if label not in labelCounts.keys(): labelCounts[label] = 0 labelCounts[label] += 1 entropy = 0.0 for key in labelCounts.keys(): p_i = float(labelCounts[key]/numEntries) entropy -= p_i * log(p_i,2)#log(x,10)表示以10 为底的对数 return entropy def split_data(data,feature_index,value): ''' 划分数据集 feature_index：用于划分特征的列数，例如“年龄” value:划分后的属性值：例如“青少年” ''' data_split=[]#划分后的数据集 for feature in data: if feature[feature_index]==value: reFeature=feature[:feature_index] reFeature.extend(feature[feature_index+1:]) data_split.append(reFeature) return data_splitdef choose_best_to_split(data): ''' 根据每个特征的信息增益，选择最大的划分数据集的索引特征 ''' count_feature=len(data[0])-1#特征个数4 #print(count_feature)#4 entropy=cal_entropy(data)#原数据总的信息熵 #print(entropy)#0.9402859586706309 max_info_gain=0.0#信息增益最大 split_fea_index = -1#信息增益最大，对应的索引号 for i in range(count_feature): feature_list=[fe_index[i] for fe_index in data]#获取该列所有特征值 ####################################### ''' print('feature_list') ['青少年', '青少年', '中年', '老年', '老年', '老年', '中年', '青少年', '青少年', '老年', '青少年', '中年', '中年', '老年'] 0.3467680694480959 #对应上篇博客中的公式 =（1）*5/14 0.3467680694480959 0.6935361388961918 ''' # print(feature_list) unqval=set(feature_list)#去除重复 Pro_entropy=0.0#特征的熵 for value in unqval:#遍历改特征下的所有属性 sub_data=split_data(data,i,value) pro=len(sub_data)/float(len(data)) Pro_entropy+=pro*cal_entropy(sub_data) #print(Pro_entropy) info_gain=entropy-Pro_entropy if(info_gain>max_info_gain): max_info_gain=info_gain split_fea_index=i return split_fea_index ##################################################def most_occur_label(labels): #sorted_label_count[0][0] 次数最多的类标签 label_count={} for label in labels: if label not in label_count.keys(): label_count[label]=0 else: label_count[label]+=1 sorted_label_count = sorted(label_count.items(),key = operator.itemgetter(1),reverse = True) return sorted_label_count[0][0]def build_decesion_tree(dataSet,featnames): ''' 字典的键存放节点信息，分支及叶子节点存放值 ''' featname = featnames[:] ################ classlist = [featvec[-1] for featvec in dataSet] #此节点的分类情况 if classlist.count(classlist[0]) == len(classlist): #全部属于一类 return classlist[0] if len(dataSet[0]) == 1: #分完了,没有属性了 return Vote(classlist) #少数服从多数 # 选择一个最优特征进行划分 bestFeat = choose_best_to_split(dataSet) bestFeatname = featname[bestFeat] del(featname[bestFeat]) #防止下标不准 DecisionTree = {bestFeatname:{}} # 创建分支,先找出所有属性值,即分支数 allvalue = [vec[bestFeat] for vec in dataSet] specvalue = sorted(list(set(allvalue))) #使有一定顺序 for v in specvalue: copyfeatname = featname[:] DecisionTree[bestFeatname][v] = build_decesion_tree(split_data(dataSet,bestFeat,v),copyfeatname) return DecisionTree

绘制可视化图的代码如下：

def getNumLeafs(myTree): '计算决策树的叶子数' # 叶子数 numLeafs = 0 # 节点信息 sides = list(myTree.keys()) firstStr =sides[0] # 分支信息 secondDict = myTree[firstStr] for key in secondDict.keys(): # 遍历所有分支 # 子树分支则递归计算 if type(secondDict[key]).__name__=='dict': numLeafs += getNumLeafs(secondDict[key]) # 叶子分支则叶子数+1 else: numLeafs +=1 return numLeafs def getTreeDepth(myTree): '计算决策树的深度' # 最大深度 maxDepth = 0 # 节点信息 sides = list(myTree.keys()) firstStr =sides[0] # 分支信息 secondDict = myTree[firstStr] for key in secondDict.keys(): # 遍历所有分支 # 子树分支则递归计算 if type(secondDict[key]).__name__=='dict': thisDepth = 1 + getTreeDepth(secondDict[key]) # 叶子分支则叶子数+1 else: thisDepth = 1 # 更新最大深度 if thisDepth > maxDepth: maxDepth = thisDepth return maxDepth import matplotlib.pyplot as plt decisionNode = dict(boxstyle="sawtooth", fc="0.8")leafNode = dict(boxstyle="round4", fc="0.8")arrow_args = dict(arrowstyle="<-") # ==================================================# 输入：# nodeTxt: 终端节点显示内容# centerPt: 终端节点坐标# parentPt: 起始节点坐标# nodeType: 终端节点样式# 输出：# 在图形界面中显示输入参数指定样式的线段(终端带节点)# ==================================================def plotNode(nodeTxt, centerPt, parentPt, nodeType): '画线(末端带一个点)' createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction', xytext=centerPt, textcoords='axes fraction', va="center", ha="center", bbox=nodeType, arrowprops=arrow_args ) # =================================================================# 输入：# cntrPt: 终端节点坐标# parentPt: 起始节点坐标# txtString: 待显示文本内容# 输出：# 在图形界面指定位置(cntrPt和parentPt中间)显示文本内容(txtString)# =================================================================def plotMidText(cntrPt, parentPt, txtString): '在指定位置添加文本' # 中间位置坐标 xMid = (parentPt[0]-cntrPt[0])/2.0 + cntrPt[0] yMid = (parentPt[1]-cntrPt[1])/2.0 + cntrPt[1] createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30) # ===================================# 输入：# myTree: 决策树# parentPt: 根节点坐标# nodeTxt: 根节点坐标信息# 输出：# 在图形界面绘制决策树# ===================================def plotTree(myTree, parentPt, nodeTxt): '绘制决策树' # 当前树的叶子数 numLeafs = getNumLeafs(myTree) # 当前树的节点信息 sides = list(myTree.keys()) firstStr =sides[0] # 定位第一棵子树的位置(这是蛋疼的一部分) cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff) # 绘制当前节点到子树节点(含子树节点)的信息 plotMidText(cntrPt, parentPt, nodeTxt) plotNode(firstStr, cntrPt, parentPt, decisionNode) # 获取子树信息 secondDict = myTree[firstStr] # 开始绘制子树，纵坐标-1。 plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD for key in secondDict.keys(): # 遍历所有分支 # 子树分支则递归 if type(secondDict[key]).__name__=='dict': plotTree(secondDict[key],cntrPt,str(key)) # 叶子分支则直接绘制 else: plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode) plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key)) # 子树绘制完毕，纵坐标+1。 plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalD # ==============================# 输入：# myTree: 决策树# 输出：# 在图形界面显示决策树# ==============================def createPlot(inTree): '显示决策树' # 创建新的图像并清空 - 无横纵坐标 fig = plt.figure(1, facecolor='white') fig.clf() axprops = dict(xticks=[], yticks=[]) createPlot.ax1 = plt.subplot(111, frameon=False, **axprops) # 树的总宽度 高度 plotTree.totalW = float(getNumLeafs(inTree)) plotTree.totalD = float(getTreeDepth(inTree)) # 当前绘制节点的坐标 plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0; # 绘制决策树 plotTree(inTree, (0.5,1.0), '') plt.show() if __name__ == '__main__': data,features=load_data() split_fea_index=choose_best_to_split(data) newtree=build_decesion_tree(data,features) print(newtree) createPlot(newtree) ''' {'age': {'old_aged': {'level': {'same': 'yes', 'good': 'no'}}, 'teenager': {'student': {'no': 'no', 'yes': 'yes'}}, 'middle_aged': 'yes'}} '''

结果如下：

怎么用决策树分类，将会在下一章。

以上就是本文的全部内容，希望对大家的学习有所帮助，也希望大家多多支持。