R语言 CART算法和C4.5算法（决策树）

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R版本：3.4.4

最新的R官网取消了mvpart包，有需要的可以留言或者加微信，我用R3.6.1版本的显示这个包不能使用。

还需要安装java环境，下载jdk,配置环境变量。

draw.tree函数：绘制树状图

J48函数：实现C4.5算法

maptree包：提供draw.tree函数

mvpart包：提供数据集car.test.frame

post函数：对rpart()结果绘制演示图

prune.rpart()：对rpart()的结果进行剪枝

rpart包：提供函数rpart()、prune.rpart()、post()

rpart.plot包提供rpart.plot函数，绘制决策时

RWeka包：提供函数J48

sampling包：strata函数用于分层抽样

#设置工作路径

> setwd('G:\\R语言\\大三下半年\\数据挖掘：R语言实战\\')
Warning message:
file ‘.RData’ has magic number 'RDX3'
Use of save versions prior to 2 is deprecated
> library(mvpart)
> data("car.test.frame")
> head(car.test.frame)
Price Country Reliability Mileage Type Weight Disp. HP
Eagle Summit 4 8895 USA 4 33 Small 2560 97 113
Ford Escort 4 7402 USA 2 33 Small 2345 114 90
Ford Festiva 4 6319 Korea 4 37 Small 1845 81 63
Honda Civic 4 6635 Japan/USA 5 32 Small 2260 91 92
Mazda Protege 4 6599 Japan 5 32 Small 2440 113 103
Mercury Tracer 4 8672 Mexico 4 26 Small 2285 97 82
> car.test.frame$Mileage <- 100*4.546/(1.6*car.test.frame$Mileage)
> names(car.test.frame) <- c("价格","产地","可靠性","油耗","类型","车重","发动机功率","净马力")
> head(car.test.frame)
价格产地可靠性油耗类型车重发动机功率净马力
Eagle Summit 4 8895 USA 4 8.609848 Small 2560 97 113
Ford Escort 4 7402 USA 2 8.609848 Small 2345 114 90
Ford Festiva 4 6319 Korea 4 7.679054 Small 1845 81 63
Honda Civic 4 6635 Japan/USA 5 8.878906 Small 2260 91 92
Mazda Protege 4 6599 Japan 5 8.878906 Small 2440 113 103
Mercury Tracer 4 8672 Mexico 4 10.927885 Small 2285 97 82

#str()函数显示该数据集有60行8列
> str(car.test.frame)
'data.frame': 60 obs. of 8 variables:
$ 价格 : int 8895 7402 6319 6635 6599 8672 7399 7254 9599 5866 ...
$ 产地 : Factor w/ 8 levels "France","Germany",..: 8 8 5 4 3 6 4 5 3 3 ...
$ 可靠性 : int 4 2 4 5 5 4 5 1 5 NA ...
$ 油耗 : num 8.61 8.61 7.68 8.88 8.88 ...
$ 类型 : Factor w/ 6 levels "Compact","Large",..: 4 4 4 4 4 4 4 4 4 4 ...
$ 车重 : int 2560 2345 1845 2260 2440 2285 2275 2350 2295 1900 ...
$ 发动机功率: int 97 114 81 91 113 97 97 98 109 73 ...
$ 净马力 : int 113 90 63 92 103 82 90 74 90 73 ...

> summary(car.test.frame)
价格产地可靠性油耗类型
Min. : 5866 USA :26 Min. :1.000 Min. : 7.679 Compact:15
1st Qu.: 9932 Japan :19 1st Qu.:2.000 1st Qu.:10.523 Large : 3
Median :12216 Japan/USA: 7 Median :3.000 Median :12.353 Medium :13
Mean :12616 Korea : 3 Mean :3.388 Mean :11.962 Small :13
3rd Qu.:14933 Germany : 2 3rd Qu.:5.000 3rd Qu.:13.530 Sporty : 9
Max. :24760 France : 1 Max. :5.000 Max. :15.785 Van : 7
(Other) : 2 NA's :11
车重发动机功率净马力
Min. :1845 Min. : 73.0 Min. : 63.0
1st Qu.:2571 1st Qu.:113.8 1st Qu.:101.5
Median :2885 Median :144.5 Median :111.5
Mean :2901 Mean :152.1 Mean :122.3
3rd Qu.:3231 3rd Qu.:180.0 3rd Qu.:142.8
Max. :3855 Max. :305.0 Max. :225.0

> #2. 数据预处理
> #下面我们着重看油耗变量，因为在以下的建模过程中，将以油耗作为目标变量
> #一个数据集来分别构建出以离散型和连续型变量为各自目标变量的分类树和回归树，考虑添加一列变量——分组油耗，即将油耗变量划分为三个组别，A:11.6~15.8个油、B:9~11.6个油、C:7.7~9个油，成为含有3个水平的A、B、C的因子变量。
> Group_Mileage=matrix(0,60,1) #设矩阵Group_Mileage用于存放新变量
> Group_Mileage[which(car.test.frame$"油耗">=11.6)]="A"
> Group_Mileage[which(car.test.frame$"油耗"<=9)]="C" #将油耗在7.7~9区间的样本Group_Mileage值取C
> Group_Mileage[which(Group_Mileage==0)]="B" #将油耗不在组A、C的样本Group_Mileage值取B
> car.test.frame$"分组油耗"=Group_Mileage #在数据集中添加新变量分组油耗
> car.test.frame[1:10,c(4,9)]
油耗分组油耗
Eagle Summit 4 8.609848 C
Ford Escort 4 8.609848 C
Ford Festiva 4 7.679054 C
Honda Civic 4 8.878906 C
Mazda Protege 4 8.878906 C
Mercury Tracer 4 10.927885 B
Nissan Sentra 4 8.609848 C
Pontiac LeMans 4 10.147321 B
Subaru Loyale 4 11.365000 B
Subaru Justy 3 8.356618 C
> a=round(1/4*sum(car.test.frame$"分组油耗"=="A"))
> b=round(1/4*sum(car.test.frame$"分组油耗"=="B"))
> c=round(1/4*sum(car.test.frame$"分组油耗"=="C"))
> #分别计算A、B、C组中应抽取测试集样本数,记为a、b、c
> a;b;c
[1] 9
[1] 4
[1] 2

#使用strata()函数对car.test.frame中的“分组油耗”变量进行分层抽样
> library(sampling)
> sub=strata(car.test.frame, stratanames="分组油耗", size=c(c,b,a), method="srswor")

> sub
分组油耗 ID_unit Prob Stratum
4 C 4 0.2222222 1
7 C 7 0.2222222 1
6 B 6 0.2500000 2
8 B 8 0.2500000 2
17 B 17 0.2500000 2
21 B 21 0.2500000 2
20 A 20 0.2571429 3
38 A 38 0.2571429 3
42 A 42 0.2571429 3
47 A 47 0.2571429 3
51 A 51 0.2571429 3
52 A 52 0.2571429 3
56 A 56 0.2571429 3
57 A 57 0.2571429 3
60 A 60 0.2571429 3
> Train_Car=car.test.frame[-sub$ID_unit,] #生成训练集
> Test_Car=car.test.frame[sub$ID_unit,] #生成测试集
> nrow(Train_Car);nrow(Test_Car) #显示训练集、测试集行数
[1] 45
[1] 15

> ##################应用案例##################
> library('rpart')

载入程辑包：‘rpart’

The following object is masked _by_ ‘.GlobalEnv’:

car.test.frame

The following objects are masked from ‘package:mvpart’:

meanvar, na.rpart, path.rpart, plotcp, post, printcp, prune, prune.rpart,
rpart, rpart.control, rsq.rpart, snip.rpart, xpred.rpart

> #1. 对油耗变量建立回归树——数字结果

#按照公式对训练集构建回归树method="anova"
> formula_Car_Reg=油耗~价格+产地+可靠性+类型+车重+发动机功率+净马力 #设定模型公式
> rp_Car_Reg=rpart(formula_Car_Reg,Train_Car,method="anova")

> print(rp_Car_Reg) #导出回归树基本信息
n= 45

node), split, n, deviance, yval
* denotes terminal node

1) root 45 186.172800 11.845280
2) 发动机功率< 134 19 32.628130 9.977205 *
3) 发动机功率>=134 26 38.786870 13.210420
6) 价格< 11522 7 3.003835 11.877100 *
7) 价格>=11522 19 18.754370 13.701630 *
#按照节点层次以不同缩进量列出，并在每条节点信息后以星号*标示出是否为叶节点。

> printcp(rp_Car_Reg) #导出回归树的cp表格

Regression tree:
rpart(formula = formula_Car_Reg, data = Train_Car, method = "anova")

Variables actually used in tree construction:
[1] 发动机功率价格

Root node error: 186.17/45 = 4.1372

n= 45

CP nsplit rel error xerror xstd
1 0.616405 0 1.00000 1.04401 0.182755
2 0.091467 1 0.38360 0.46353 0.075249
3 0.010000 2 0.29213 0.42704 0.063786

#获取决策树rp_Car_Reg详细信息，Variable importance变量的最要程度、improve对分支的提升程度
> summary(rp_Car_Reg)
Call:
rpart(formula = formula_Car_Reg, data = Train_Car, method = "anova")
n= 45

CP nsplit rel error xerror xstd
1 0.61640483 0 1.0000000 1.0440087 0.18275540
2 0.09146694 1 0.3835952 0.4635295 0.07524941
3 0.01000000 2 0.2921282 0.4270404 0.06378585

Variable importance
发动机功率车重价格净马力类型产地
26 20 14 14 13 12

Node number 1: 45 observations, complexity param=0.6164048
mean=11.84528, MSE=4.137174
left son=2 (19 obs) right son=3 (26 obs)
Primary splits:
发动机功率 < 134 to the left, improve=0.6164048, (0 missing)
价格 < 9446.5 to the left, improve=0.5563919, (0 missing)
车重 < 2567.5 to the left, improve=0.5509927, (0 missing)
类型 splits as RRRLRR, improve=0.4392540, (0 missing)
净马力 < 109 to the left, improve=0.3982844, (0 missing)
Surrogate splits:
车重 < 2747.5 to the left, agree=0.889, adj=0.737, (0 split)
净马力 < 109 to the left, agree=0.800, adj=0.526, (0 split)
类型 splits as RRRLRR, agree=0.778, adj=0.474, (0 split)
价格 < 9446.5 to the left, agree=0.756, adj=0.421, (0 split)
产地 splits as LLLLR-RR, agree=0.756, adj=0.421, (0 split)

Node number 2: 19 observations
mean=9.977205, MSE=1.71727

Node number 3: 26 observations, complexity param=0.09146694
mean=13.21042, MSE=1.491803
left son=6 (7 obs) right son=7 (19 obs)
Primary splits:
价格 < 11522 to the left, improve=0.4390315, (0 missing)
车重 < 3087.5 to the left, improve=0.3622234, (0 missing)
类型 splits as LRL-RR, improve=0.3121080, (0 missing)
发动机功率 < 185.5 to the left, improve=0.1511378, (0 missing)
净马力 < 148.5 to the left, improve=0.1511378, (0 missing)
Surrogate splits:
车重 < 2757.5 to the left, agree=0.846, adj=0.429, (0 split)
产地 splits as --RLL-RR, agree=0.808, adj=0.286, (0 split)
类型 splits as LRR-RR, agree=0.808, adj=0.286, (0 split)
净马力 < 103.5 to the left, agree=0.808, adj=0.286, (0 split)
发动机功率 < 142 to the left, agree=0.769, adj=0.143, (0 split)

Node number 6: 7 observations
mean=11.8771, MSE=0.4291194

Node number 7: 19 observations
mean=13.70163, MSE=0.9870723

> #下面我们尝试改变rpart()函数的若干参数值，minsplit=10，将分支包含最小样本数minsplit从默认值20改为10，新的回归树记为rp_Car_Reg1。
> rp_Car_Reg1=rpart(formula_Car_Reg,Train_Car,method="anova",minsplit=10)

> print(rp_Car_Reg1) #导出回归树基本信息
n= 45

node), split, n, deviance, yval
* denotes terminal node

1) root 45 186.172800 11.845280
2) 发动机功率< 134 19 32.628130 9.977205
4) 价格< 9504.5 8 2.649246 8.582424 *
5) 价格>=9504.5 11 3.096802 10.991590 *
3) 发动机功率>=134 26 38.786870 13.210420
6) 价格< 11522 7 3.003835 11.877100 *
7) 价格>=11522 19 18.754370 13.701630
14) 类型=Compact,Medium 12 2.880021 13.081890 *
15) 类型=Large,Sporty,Van 7 3.364168 14.764060 *
> printcp(rp_Car_Reg1) #导出回归树的cp表格

Regression tree:
rpart(formula = formula_Car_Reg, data = Train_Car, method = "anova",
minsplit = 10)

Variables actually used in tree construction:
[1] 发动机功率价格类型

Root node error: 186.17/45 = 4.1372

n= 45

CP nsplit rel error xerror xstd
1 0.616405 0 1.000000 1.04535 0.183175
2 0.144393 1 0.383595 0.46279 0.074342
3 0.091467 2 0.239202 0.36798 0.080715
4 0.067197 3 0.147735 0.38852 0.111059
5 0.010000 4 0.080538 0.32070 0.111356

#cp值表示可以使模型拟合程度提高的节点，剪去不重要的分支

> rp_Car_Reg2=rpart(formula_Car_Reg,Train_Car,method="anova",cp=0.1)
> #将CP值从默认的0.01改为0.1，新的回归树记为rp_Car_Reg2
> print(rp_Car_Reg2) #导出回归树基本信息
n= 45

node), split, n, deviance, yval
* denotes terminal node

1) root 45 186.17280 11.845280
2) 发动机功率< 134 19 32.62813 9.977205 *
3) 发动机功率>=134 26 38.78687 13.210420 *
> printcp(rp_Car_Reg2) #导出回归树的cp表格

Regression tree:
rpart(formula = formula_Car_Reg, data = Train_Car, method = "anova",
cp = 0.1)

Variables actually used in tree construction:
[1] 发动机功率

Root node error: 186.17/45 = 4.1372

n= 45

CP nsplit rel error xerror xstd
1 0.6164 0 1.0000 1.07992 0.189818
2 0.1000 1 0.3836 0.47707 0.078252
> #剪枝函数也可以实现同样的效果
> rp_Car_Reg3=prune.rpart(rp_Car_Reg,cp=0.1)
> print(rp_Car_Reg3)
n= 45

node), split, n, deviance, yval
* denotes terminal node

1) root 45 186.17280 11.845280
2) 发动机功率< 134 19 32.62813 9.977205 *
3) 发动机功率>=134 26 38.78687 13.210420 *
> printcp(rp_Car_Reg3)

Regression tree:
rpart(formula = formula_Car_Reg, data = Train_Car, method = "anova")

Variables actually used in tree construction:
[1] 发动机功率

Root node error: 186.17/45 = 4.1372

n= 45

CP nsplit rel error xerror xstd
1 0.6164 0 1.0000 1.04401 0.182755
2 0.1000 1 0.3836 0.46353 0.075249
> #对所生成树的大小也可以通过深度函数maxdepth来控制
> rp_Car_Reg4=rpart(formula_Car_Reg,Train_Car,method="anova",maxdepth=1)
> print(rp_Car_Reg4)
n= 45

node), split, n, deviance, yval
* denotes terminal node

1) root 45 186.17280 11.845280
2) 发动机功率< 134 19 32.62813 9.977205 *
3) 发动机功率>=134 26 38.78687 13.210420 *
> printcp(rp_Car_Reg4)

Regression tree:
rpart(formula = formula_Car_Reg, data = Train_Car, method = "anova",
maxdepth = 1)

Variables actually used in tree construction:
[1] 发动机功率

Root node error: 186.17/45 = 4.1372

n= 45

CP nsplit rel error xerror xstd
1 0.6164 0 1.0000 1.09740 0.191557
2 0.0100 1 0.3836 0.52651 0.084732

#2. 对油耗变量建立回归树——树形结果
> rp_Car_Plot=rpart(formula_Car_Reg,Train_Car,method="anova",minsplit=10)
> #设置minsplit为10，新的回归树记为rp_Car_Plot
> print(rp_Car_Plot)
n= 45

node), split, n, deviance, yval
* denotes terminal node

> rpart.plot(rp_Car_Plot,type=4) #更改type参数为类型4，绘制决策树
> #每一分支的取值范围也被标示出来，而且在每个节点的油耗的预测值也被标出
> #当树的分支较多时，我们还可以选择设置“分支”参数branch=1来获得垂直枝干形状的决策
> #树以减少图形所占空间，使得树状图的枝干不再显得杂乱无章，更方便查看和分析。

> rpart.plot(rp_Car_Plot,type=4,branch=1)
> #参数fallen.leaves设置为TRUE，即表示将所有叶节点一致的摆放在树的最下端
> rpart.plot(rp_Car_Plot,type=4,branch=1,fallen.leaves=TRUE)
> library(maptree)
载入需要的程辑包：cluster
> draw.tree(rp_Car_Plot, col=rep(1,8), nodeinfo=TRUE)#利用draw.tree()绘制决策树

> plot(rp_Car_Plot,uniform=TRUE,main="plot: Regression TRUE")
> text(rp_Car_Plot,use.n=TRUE,all=TRUE)#用plot()直接绘图，并在图中添加相关文字信息

> post(rp_Car_Plot,file="") #用post()函数绘制决策树

> #3. 对分组油耗变量建立分类树
> formula_Car_Cla=分组油耗~价格+产地+可靠性+类型+车重+发动机功率+净马力
> rp_Car_Cla=rpart(formula_Car_Cla, Train_Car, method="class", minsplit=5)
> #按公式formula_Car_Cla对训练集创建分类树
> print(rp_Car_Cla)
n= 45

node), split, n, loss, yval, (yprob)
* denotes terminal node

1) root 45 19 A (0.57777778 0.26666667 0.15555556)
2) 发动机功率>=134 26 2 A (0.92307692 0.07692308 0.00000000)
4) 价格>=11222 20 0 A (1.00000000 0.00000000 0.00000000) *
5) 价格< 11222 6 2 A (0.66666667 0.33333333 0.00000000)
10) 发动机功率< 152 4 0 A (1.00000000 0.00000000 0.00000000) *
11) 发动机功率>=152 2 0 B (0.00000000 1.00000000 0.00000000) *
3) 发动机功率< 134 19 9 B (0.10526316 0.52631579 0.36842105)
6) 价格>=9504.5 11 2 B (0.18181818 0.81818182 0.00000000) *
7) 价格< 9504.5 8 1 C (0.00000000 0.12500000 0.87500000) *
> #以上输出结果与回归树类似，不同之处仅在于每个节点的预测值不再是具体数值，而是A、B、C，即分组油耗的三个取值水平。
> rpart.plot(rp_Car_Cla, type=4, fallen.leaves=TRUE) #对rp_Car_Cla绘制分类树

#发动机高于134的且价格高于1万美元的车，属于A类，高油耗；最左边的分支，反之属于C类，最右侧分支。

#4. 对测试集Test_Car预测目标变量
> pre_Car_Cla=predict(rp_Car_Cla,Test_Car,type="class")
> #对测试集Test_Car中观测样本中的分组油耗指标进行预测
> pre_Car_Cla #显示预测结果
Honda Civic 4 Nissan Sentra 4 Mercury Tracer 4 Pontiac LeMans 4
C C C C
Ford Probe Plymouth Laser Nissan 240SX 4 Acura Legend V6
B B A A
Eagle Premier V6 Nissan Maxima V6 Buick Le Sabre V6 Chevrolet Caprice V8
A A A A
Ford Aerostar V6 Mazda MPV V6 Nissan Van 4
A A A
Levels: A B C
> (p=sum(as.numeric(pre_Car_Cla!=Test_Car$"分组油耗"))/nrow(Test_Car)) #计算错误率
[1] 0.1333333
> table(Test_Car$"分组油耗", pre_Car_Cla) #获取混淆矩阵
pre_Car_Cla
A B C
A 9 0 0
B 0 2 2
C 0 0 2

######################## C4.5应用 ###################

> #C4.5算法仅适用离散变量，即构建分类树，因此这里我们就继续沿用上面的数据集来对分组油
> #耗指标进行建树。需要说明的是，用于实现C4.5算法的核心函数J48()对中文识别不太完善，因此我们将使用原
> #英文数据集中的变量名称。#“价格(Price)”、产地(Country)、可靠性(Reliability)、英里数(Mileage)、类型(Type)、
> #车重(Weight)、发动机功率(Disp.)，以及净马力(HP)，分组油耗(Oil_Consumption)。
> #install.packages("rJava")
> library(RWeka)
> names(Train_Car)=c("Price","Country","Reliability","Mileage","Type","Weight","Disp.",
+ "HP","Oil_Consumption") #更改为英文变量名
> Train_Car$Oil_Consumption=as.factor(Train_Car$Oil_Consumption)
> #将分组哟好的变量类型改为因子型，使J48()函数可识别
> formula=Oil_Consumption~Price+Country+Reliability+Type+Weight+Disp.+HP
> C45_0=J48(formula,Train_Car) #在默认参数去之下，构建分类树模型C45_0
> C45_0
J48 pruned tree
------------------

Number of Leaves : 5

Size of the tree : 9

> #共计10个叶节点，15个节点，最后括号中的数字表示有多少观测样本被归入该分支，且其中有
> #几个是被错分的。
> summary(C45_0)

=== Summary ===

Correctly Classified Instances 34 94.4444 %
Incorrectly Classified Instances 2 5.5556 %
Kappa statistic 0.9045
Mean absolute error 0.0595
Root mean squared error 0.1725
Relative absolute error 15.067 %
Root relative squared error 39.0042 %
Total Number of Instances 36

=== Confusion Matrix ===

a b c <-- classified as
20 0 0 | a = A
1 8 1 | b = B
0 0 6 | c = C
> #下面我们通过control参数控制分类树的生成过程。参数M,即对每个叶节点设置最小观测样本
> #量来对树进行剪枝。我们知道，M的默认值为2，现在将其取值为3来减去若干所含样本量较小
> #的分支。
> C45_1=J48(formula,Train_Car,control=Weka_control(M=3))
> #取control参数的M值为3，构建分类树模型C45_1
> C45_1
J48 pruned tree
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Price <= 9410: C (7.0/1.0)
Price > 9410
| Disp. <= 132: B (6.0)
| Disp. > 132: A (23.0/3.0)

Number of Leaves : 3

Size of the tree : 5

> plot(C45_1) #对C45_1绘制分类树