【机器学习】决策树——决策树的两种实现方式（Python版）-原创手记-慕课网

从周志华的机器学习中，我们可以得到基于信息增益准则的决策树构建算法：

输入：训练集 $D=\{(x_1,y_1),(x_2,y_2),\cdots,(x_m,y_m)\}$
属性集 $A=\{a_1,a_2,\cdots,a_d\}$
过程：函数 $createTree(D,A)$ 的实现
1. 生成结点node;
2. if $D$ 中样本全属于同一类别 $C$ then
3. 将node标记为 $C$ 类叶结点；return
4. end if
5. if $A=\varnothing$ OR $D$ 中样本在 $A$ 上取值相同 then
6. 将node标记为叶结点，其类别标记为 $D$ 中样本数最多的类；return
7. end if
8. 从 $A$ 中选择最优划分属性 $a_*$ （信息增益或者其他算法准则）；
9. for $a_*$ 的每一个值 $a_*^v$ do
10. 为node生成一个分支；令 $D_v$ 表示 $D$ 中在 $a_*$ 上取值为 $a_*^v$ 的样本子集；
11. if $D_v$ 为空 then
12. 将分支结点标记为叶结点，其类别标记为 $D$ 中样本最多的类；return
13. else
14. 以 $createTree(D_v,A/\{a_*\})$ 为分支结点
15. end if
16. end for
输出：以node为根节点的一棵决策树

故，基于信息增益的决策树算法的实现代码如下：

#!/usr/bin/env python3
# -*- coding: utf-8 -*-
"""
Created on Mon Oct 29 20:15:21 2018

@author: lxh
"""
#决策树的实现

from math import log
import time

def createDataSet():
    dataSet =[[1,1,'yes'],[1,1,'yes'],[1,0,'no'],[0,1,'no'],[0,1,'no'],]
    labels =['Tree','leaves']
    return dataSet,labels

#计算香农熵
def calcShannonEnt(dataSet):
    numEntries =len(dataSet)
    labelCounts={}
    for feaVec in dataSet:
        currentLabel =feaVec[-1]
        if currentLabel not in labelCounts:
            labelCounts[currentLabel]=0
        labelCounts[currentLabel]+=1
    shannonEnt =0.0
    for key in labelCounts:
        prob =float(labelCounts[key])/numEntries
        shannonEnt-=prob*log(prob,2)
    return shannonEnt

#去掉已经决策过的属性
def splitDataSet(dataSet,axis,value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis]==value:
            reducedFeatVec =featVec[:axis]
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

#根据信息增益算法，选取最优属性
def chooseBestFeatureToSplit(dataSet):
    numFeatures = len(dataSet[0])-1 #因为数据集的最后一项是标签
    baseEntropy = calcShannonEnt(dataSet)
    bestInfoGain =0.0
    bestFeature = -1
    for i in range(numFeatures):
        featList =[example[i] for example in dataSet]
        print(featList)
        uniqueVals =set(featList)
        newEntropy = 0.0
        for value in uniqueVals:
            subDataSet =splitDataSet(dataSet,i,value)
            prob = len(subDataSet)/float(len(dataSet))
            newEntropy +=prob * calcShannonEnt(subDataSet)
        infoGain = baseEntropy -newEntropy
        if infoGain >bestInfoGain:
            bestInfoGain =infoGain
            bestFeature =i
    return bestFeature
#因为我们递归构建决策树是根据属性的消耗进行计算的，所以可能会存在最后属性用完了，但是分类还没有算完，
#这时候就会采用多数表决的方式计算节点分类
def majorityCnt(classList):
    classCount ={}
    for vote in classList:
        if vote not in classCount.keys():
            classCount[vote] =0
        classCount[vote]+=1
    return max(classCount)

def createTree(dataSet,labels):
    classList =[example[-1] for example in dataSet]
    if classList.count(classList[0]) ==len(classList): #类别相同则停止划分
        return classList[0]
    if len(dataSet[0])==1:#所有特征已经用完
        return majorityCnt(classList)
    bestFeat = chooseBestFeatureToSplit(dataSet)
    bestFeatLabel =labels[bestFeat]
    myTree ={bestFeatLabel:{}}
    del(labels[bestFeat])
    featValues = [example[bestFeat] for example in dataSet]
    uniqueVals = set(featValues)
    for value in uniqueVals:
        subLabels = labels[:]#为了不改变原始列表的内容复制了一下
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet,bestFeat, value),subLabels)
    return myTree
     
def main():
    data,label =createDataSet()
    t1 =time.clock()
    myTree =createTree(data,label)
    t2 =time.clock()
    print(myTree)
    print('execure time:',t2-t1)


if __name__=='__main__':
    main()

【基于scikit-learn的决策树实现】

scikit-learn库为我们提供了实现决策树算法的接口，我们可以通过调用接口进行代码实现，本部分代码除了包含决策树代码以外，还包含：随机森林、决策树可视化、参数自动选择等代码。具体如下（jupyer）：

%matplotlib inline
import matplotlib.pyplot as plt
import pandas as pd

from sklearn.datasets.california_housing import fetch_california_housing
housing = fetch_california_housing()
print(housing.DESCR)

housing.data.shape
housing.data[0]

from sklearn import tree
dtr = tree.DecisionTreeRegressor(max_depth = 2)
dtr.fit(housing.data[:, [6, 7]], housing.target)

#要可视化显示 首先需要安装 graphviz   http://www.graphviz.org/Download..php
dot_data = \
    tree.export_graphviz(
        dtr,
        out_file = None,
        feature_names = housing.feature_names[6:8],
        filled = True,
        impurity = False,
        rounded = True
    )
#可视化展示决策树
#pip install pydotplus
import pydotplus
graph = pydotplus.graph_from_dot_data(dot_data)
graph.get_nodes()[7].set_fillcolor("#FFF2DD")
from IPython.display import Image
Image(graph.create_png())
#保存图片
graph.write_png("dtr_white_background.png")

#随机森林算法
from sklearn.model_selection import train_test_split
data_train, data_test, target_train, target_test = \
    train_test_split(housing.data, housing.target, test_size = 0.1, random_state = 42)
dtr = tree.DecisionTreeRegressor(random_state = 42)
dtr.fit(data_train, target_train)

dtr.score(data_test, target_test)

from sklearn.ensemble import RandomForestRegressor
rfr = RandomForestRegressor( random_state = 42)
rfr.fit(data_train, target_train)
rfr.score(data_test, target_test)

#参数自动化匹配
from sklearn.grid_search import GridSearchCV
tree_param_grid = { 'min_samples_split': list((3,6,9)),'n_estimators':list((10,50,100))}
grid = GridSearchCV(RandomForestRegressor(),param_grid=tree_param_grid, cv=5)
grid.fit(data_train, target_train)
grid.grid_scores_, grid.best_params_, grid.best_score_

rfr = RandomForestRegressor( min_samples_split=3,n_estimators = 100,random_state = 42)
rfr.fit(data_train, target_train)
rfr.score(data_test, target_test)

pd.Series(rfr.feature_importances_, index = housing.feature_names).sort_values(ascending = False)

决策树可视化结果如下所示：
图片描述