python实现决策树分类（二）

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 np
import pandas as pd
from math import log
import 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_split
def 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，将会在下一章介绍python实现决策树分类（三）