机器学习/数据分析--通俗语言带你入门决策树(结合分类和回归案例)

羊小猪~~2024-08-27 6:10

前言

  • 机器学习是深度学习和数据分析的基础，接下来将更新常见的机器学习算法
  • 注意：在打数学建模比赛中，机器学习用的也很多，可以一起学习
  • 决策树模型数学原理很复杂，强烈推荐看书，看书，看书，这里推荐《统计学习方法》和《机器学习西瓜书》。
  • 这里只是介绍了决策树组成，但是原理没有详细介绍，后面会出详介绍篇章。
  • 最近开学，更新不太及时，请大家见谅，欢迎收藏 + 点赞 + 关注

文章目录

决策树模型

简介

定义(统计学习方法) ：分类决策树模型是一种描述对实例进行分类的树形结构，决策树由节点、有向边组成，节点类型有两种，内部节点和叶子节点，内部节点 表示一个特征或者属性，叶子节点表示一个类。

决策树与if-then：

学过任何语言的人都知道if-else结构，决策树也是这样，如果if满足某一种条件，则归到一类 ，不满足条件的归到另外一类 ，如此循环判断，一直到所有特征、属性和类都归类到某一类，最终形成一颗树 ，注意 ：一个原则互斥且完备。

决策树过程：

特征选择、建立决策树、决策树剪枝三个过程

决策树解决问题：

回归和分类，如果分类的叶子节点，就是回归，否则就是分类。

建立决策树的方法

决策树背后由很多的数学原理 ，这里只介绍信息增益、信息增益比、基尼系数 ，其他的概念推荐翻阅统计学习方法 和西瓜书，想要电子版资料的可以私聊我。

建议：这一部分一定要看书，推荐统计学习方法和机器学习西瓜书，书中有很详细的案例帮助我们理解。67y

以下概念均来自于《统计学习方法》

信息增益 ： 特征A对训练数据集D的信息增益g(D.A)，定义为集合D的经验熵H(D)与特征A给定条件下D的经验条件H(DA)之差，即：

​ g ( D , A ) = H ( D ) − H ( D ∣ A ) g\left(D,A\right)=H\left(D\right)-H\left(D|A\right) g(D,A)=H(D)−H(D∣A)

信息增益比 ：特征A对训练数据集D的信息增益比gR(D)定为其信息增益 g(D,A)与训练数据集 D 关于特征 A的值的熵 HA(D)之比。即：

​ g R ( D , A ) = g ( D , A ) H A ( D ) g_{R}(D,A)=\frac{g(D,A)}{H_{A}(D)} gR(D,A)=HA(D)g(D,A)

其中： H A ( D ) = − ∑ i = 1 n ∣ D i ∣ ∣ D ∣ log ⁡ 2 ∣ D i ∣ ∣ D ∣ H_{A}(D)=-\sum_{i=1}^{n}\frac{\left|D_{i}\right|}{\left|D\right|}\log_{2}\frac{\left|D_{i}\right|}{\left|D\right|} HA(D)=−i=1∑n∣D∣∣Di∣log2∣D∣∣Di∣ ，n表示特征A的数量。

基尼指数：分类问题中，假设有区个类，样本点属于第k 类的概率为 pk，则概率分布的基尼指数定义为：

​ G i n i ( p ) = ∑ k = 1 K p k ( 1 − p k ) = 1 − ∑ k = 1 K p k 2 Gini\left(p\right)=\sum_{k=1}^{K}p_{k}\left(1-p_{k}\right)=1-\sum_{k=1}^{K}p_{k}^{2} Gini(p)=k=1∑Kpk(1−pk)=1−k=1∑Kpk2

建议：看书，通过案例和公式来理解。

分类案例

简介：通过鸢尾花的叶子特征，构建判别叶子类别的树。

导入数据和数据分析

python 复制代码 
import numpy as np 
import pandas as pd 

url = "https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data" 
columns = ['花萼-length', '花萼-width', '花瓣-length', '花瓣-width', 'class']

data = pd.read_csv(url, names=columns)
data

| | 花萼-length | 花萼-width | 花瓣-length | 花瓣-width | class |
| 0 | 5.1 | 3.5 | 1.4 | 0.2 | Iris-setosa |
| 1 | 4.9 | 3.0 | 1.4 | 0.2 | Iris-setosa |
| 2 | 4.7 | 3.2 | 1.3 | 0.2 | Iris-setosa |
| 3 | 4.6 | 3.1 | 1.5 | 0.2 | Iris-setosa |
| 4 | 5.0 | 3.6 | 1.4 | 0.2 | Iris-setosa |
| ... | ... | ... | ... | ... | ... |
| 145 | 6.7 | 3.0 | 5.2 | 2.3 | Iris-virginica |
| 146 | 6.3 | 2.5 | 5.0 | 1.9 | Iris-virginica |
| 147 | 6.5 | 3.0 | 5.2 | 2.0 | Iris-virginica |
| 148 | 6.2 | 3.4 | 5.4 | 2.3 | Iris-virginica |

149 5.9 3.0 5.1 1.8 Iris-virginica

150 rows × 5 columns

python 复制代码 
# 查看值的类别和数量
data['class'].value_counts()

结果：

class
Iris-setosa        50
Iris-versicolor    50
Iris-virginica     50
Name: count, dtype: int64
python 复制代码 
# 查看变量信息
data.info()
<class 'pandas.core.frame.DataFrame'>
RangeIndex: 150 entries, 0 to 149
Data columns (total 5 columns):
 #   Column     Non-Null Count  Dtype  
---  ------     --------------  -----  
 0   花萼-length  150 non-null    float64
 1   花萼-width   150 non-null    float64
 2   花瓣-length  150 non-null    float64
 3   花瓣-width   150 non-null    float64
 4   class      150 non-null    object 
dtypes: float64(4), object(1)
memory usage: 6.0+ KB
python 复制代码 
# 查看缺失值
data.isnull().sum()

结果：

花萼-length    0
花萼-width     0
花瓣-length    0
花瓣-width     0
class        0
dtype: int64
python 复制代码 
# 查看特征的统计变量
data.describe()

结果：

| | 花萼-length | 花萼-width | 花瓣-length | 花瓣-width |
| count | 150.000000 | 150.000000 | 150.000000 | 150.000000 |
| mean | 5.843333 | 3.054000 | 3.758667 | 1.198667 |
| std | 0.828066 | 0.433594 | 1.764420 | 0.763161 |
| min | 4.300000 | 2.000000 | 1.000000 | 0.100000 |
| 25% | 5.100000 | 2.800000 | 1.600000 | 0.300000 |
| 50% | 5.800000 | 3.000000 | 4.350000 | 1.300000 |
| 75% | 6.400000 | 3.300000 | 5.100000 | 1.800000 |

max 7.900000 4.400000 6.900000 2.500000
python 复制代码 
# 查看特征变量的相关性
name_corr = ['花萼-length', '花萼-width', '花瓣-length', '花瓣-width']
corr = data[name_corr].corr()
print(corr)
           花萼-length  花萼-width  花瓣-length  花瓣-width
花萼-length   1.000000 -0.109369   0.871754  0.817954
花萼-width   -0.109369  1.000000  -0.420516 -0.356544
花瓣-length   0.871754 -0.420516   1.000000  0.962757
花瓣-width    0.817954 -0.356544   0.962757  1.000000

说明：特征变量之间存在共线性问题

划分自变量和因变量

python 复制代码 
X = data.iloc[:, [0, 1, 2, 3]].values   # .values转化成矩阵
y = data.iloc[:, 4].values

模型训练

python 复制代码 
from sklearn import tree

model = tree.DecisionTreeClassifier()
model.fit(X, y)   # 模型训练
python 复制代码 
# 打印模型结构
r = tree.export_text(model)

模型预测结果

python 复制代码 
# 随机选取值
x_test = X[[0, 30, 60, 90, 120, 130], :]
y_pred_prob = model.predict_proba(x_test)   # 预测概率
y_pred = model.predict(x_test)     # 预测值
python 复制代码 
print("\n===模型===")
print(r)
===模型===
|--- feature_3 <= 0.80
|   |--- class: Iris-setosa
|--- feature_3 >  0.80
|   |--- feature_3 <= 1.75
|   |   |--- feature_2 <= 4.95
|   |   |   |--- feature_3 <= 1.65
|   |   |   |   |--- class: Iris-versicolor
|   |   |   |--- feature_3 >  1.65
|   |   |   |   |--- class: Iris-virginica
|   |   |--- feature_2 >  4.95
|   |   |   |--- feature_3 <= 1.55
|   |   |   |   |--- class: Iris-virginica
|   |   |   |--- feature_3 >  1.55
|   |   |   |   |--- feature_2 <= 5.45
|   |   |   |   |   |--- class: Iris-versicolor
|   |   |   |   |--- feature_2 >  5.45
|   |   |   |   |   |--- class: Iris-virginica
|   |--- feature_3 >  1.75
|   |   |--- feature_2 <= 4.85
|   |   |   |--- feature_0 <= 5.95
|   |   |   |   |--- class: Iris-versicolor
|   |   |   |--- feature_0 >  5.95
|   |   |   |   |--- class: Iris-virginica
|   |   |--- feature_2 >  4.85
|   |   |   |--- class: Iris-virginica
python 复制代码 
print("\n===测试数据===")
print(x_test)
===测试数据===
[[5.1 3.5 1.4 0.2]
 [4.8 3.1 1.6 0.2]
 [5.  2.  3.5 1. ]
 [5.5 2.6 4.4 1.2]
 [6.9 3.2 5.7 2.3]
 [7.4 2.8 6.1 1.9]]
python 复制代码 
print("\n===预测所属类别概率===")
print(y_pred_prob)
===预测所属类别概率===
[[1. 0. 0.]
 [1. 0. 0.]
 [0. 1. 0.]
 [0. 1. 0.]
 [0. 0. 1.]
 [0. 0. 1.]]
python 复制代码 
print("\n===测试所属类别==")
print(y_pred)
===测试所属类别==
['Iris-setosa' 'Iris-setosa' 'Iris-versicolor' 'Iris-versicolor'
 'Iris-virginica' 'Iris-virginica']

回归案例

通过鸢尾花三个特征，预测花瓣长度。

导入数据

python 复制代码 
import pandas as pd 
import numpy as np 

url = "https://archive.ics.uci.edu/ml/machine-learning-databases/iris/iris.data"
names = ['花萼-width', '花萼-length', '花瓣-width', '花瓣-length', 'class']

data = pd.read_csv(url, names=names)
data

| | 花萼-width | 花萼-length | 花瓣-width | 花瓣-length | class |
| 0 | 5.1 | 3.5 | 1.4 | 0.2 | Iris-setosa |
| 1 | 4.9 | 3.0 | 1.4 | 0.2 | Iris-setosa |
| 2 | 4.7 | 3.2 | 1.3 | 0.2 | Iris-setosa |
| 3 | 4.6 | 3.1 | 1.5 | 0.2 | Iris-setosa |
| 4 | 5.0 | 3.6 | 1.4 | 0.2 | Iris-setosa |
| ... | ... | ... | ... | ... | ... |
| 145 | 6.7 | 3.0 | 5.2 | 2.3 | Iris-virginica |
| 146 | 6.3 | 2.5 | 5.0 | 1.9 | Iris-virginica |
| 147 | 6.5 | 3.0 | 5.2 | 2.0 | Iris-virginica |
| 148 | 6.2 | 3.4 | 5.4 | 2.3 | Iris-virginica |

149 5.9 3.0 5.1 1.8 Iris-virginica

150 rows × 5 columns

划分数据

python 复制代码 
# 划分数据
X = data.iloc[:, [0, 1, 2]]
y = data.iloc[:, 3]

创建模型

python 复制代码 
from sklearn import tree 

model = tree.DecisionTreeRegressor()
model.fit(X, y)   # 模型训练

模型预测与训练

python 复制代码 
x_test = X.iloc[[0, 1, 50, 51, 100, 120], :]
y_test = y.iloc[[0, 1, 50, 51, 100, 120]]   # 只有一列

y_pred = model.predict(x_test)

模型评估

python 复制代码 
# 输出原始值和真实值
df = pd.DataFrame()
df['原始值'] = y_test 
df['预测值'] = y_pred

df

| | 原始值 | 预测值 |
| 0 | 0.2 | 0.25 |
| 1 | 0.2 | 0.20 |
| 50 | 1.4 | 1.40 |
| 51 | 1.5 | 1.50 |
| 100 | 2.5 | 2.50 |

120 2.3 2.30
python 复制代码 
from sklearn.metrics import mean_absolute_error
# 误差计算
mse = mean_absolute_error(y_test, y_pred)
mse

结果：

0.008333333333333331
python 复制代码 
# 打印树结构
r = tree.export_text(model)
print(r)
# 树模型结构比较复杂，可以运行后面代码绘图展示。
|--- feature_2 <= 2.45
|   |--- feature_1 <= 3.25
|   |   |--- feature_1 <= 2.60
|   |   |   |--- value: [0.30]
|   |   |--- feature_1 >  2.60
|   |   |   |--- feature_0 <= 4.85
|   |   |   |   |--- feature_0 <= 4.35
|   |   |   |   |   |--- value: [0.10]
|   |   |   |   |--- feature_0 >  4.35
|   |   |   |   |   |--- feature_2 <= 1.35
|   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |--- feature_2 >  1.35
|   |   |   |   |   |   |--- feature_1 <= 2.95
|   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |--- feature_1 >  2.95
|   |   |   |   |   |   |   |--- feature_0 <= 4.65
|   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |   |--- feature_0 >  4.65
|   |   |   |   |   |   |   |   |--- feature_1 <= 3.05
|   |   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |   |   |--- feature_1 >  3.05
|   |   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |--- feature_0 >  4.85
|   |   |   |   |--- feature_0 <= 4.95
|   |   |   |   |   |--- feature_1 <= 3.05
|   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |--- feature_1 >  3.05
|   |   |   |   |   |   |--- value: [0.10]
|   |   |   |   |--- feature_0 >  4.95
|   |   |   |   |   |--- value: [0.20]
|   |--- feature_1 >  3.25
|   |   |--- feature_2 <= 1.55
|   |   |   |--- feature_1 <= 4.30
|   |   |   |   |--- feature_1 <= 3.95
|   |   |   |   |   |--- feature_1 <= 3.85
|   |   |   |   |   |   |--- feature_1 <= 3.65
|   |   |   |   |   |   |   |--- feature_0 <= 5.30
|   |   |   |   |   |   |   |   |--- feature_2 <= 1.45
|   |   |   |   |   |   |   |   |   |--- feature_1 <= 3.55
|   |   |   |   |   |   |   |   |   |   |--- feature_2 <= 1.35
|   |   |   |   |   |   |   |   |   |   |   |--- value: [0.30]
|   |   |   |   |   |   |   |   |   |   |--- feature_2 >  1.35
|   |   |   |   |   |   |   |   |   |   |   |--- truncated branch of depth 3
|   |   |   |   |   |   |   |   |   |--- feature_1 >  3.55
|   |   |   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |   |   |--- feature_2 >  1.45
|   |   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |   |--- feature_0 >  5.30
|   |   |   |   |   |   |   |   |--- feature_1 <= 3.45
|   |   |   |   |   |   |   |   |   |--- value: [0.40]
|   |   |   |   |   |   |   |   |--- feature_1 >  3.45
|   |   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |--- feature_1 >  3.65
|   |   |   |   |   |   |   |--- feature_0 <= 5.20
|   |   |   |   |   |   |   |   |--- feature_1 <= 3.75
|   |   |   |   |   |   |   |   |   |--- value: [0.40]
|   |   |   |   |   |   |   |   |--- feature_1 >  3.75
|   |   |   |   |   |   |   |   |   |--- value: [0.30]
|   |   |   |   |   |   |   |--- feature_0 >  5.20
|   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |--- feature_1 >  3.85
|   |   |   |   |   |   |--- value: [0.40]
|   |   |   |   |--- feature_1 >  3.95
|   |   |   |   |   |--- feature_0 <= 5.35
|   |   |   |   |   |   |--- value: [0.10]
|   |   |   |   |   |--- feature_0 >  5.35
|   |   |   |   |   |   |--- value: [0.20]
|   |   |   |--- feature_1 >  4.30
|   |   |   |   |--- value: [0.40]
|   |   |--- feature_2 >  1.55
|   |   |   |--- feature_0 <= 4.90
|   |   |   |   |--- value: [0.20]
|   |   |   |--- feature_0 >  4.90
|   |   |   |   |--- feature_0 <= 5.05
|   |   |   |   |   |--- feature_1 <= 3.45
|   |   |   |   |   |   |--- value: [0.40]
|   |   |   |   |   |--- feature_1 >  3.45
|   |   |   |   |   |   |--- value: [0.60]
|   |   |   |   |--- feature_0 >  5.05
|   |   |   |   |   |--- feature_1 <= 3.35
|   |   |   |   |   |   |--- value: [0.50]
|   |   |   |   |   |--- feature_1 >  3.35
|   |   |   |   |   |   |--- feature_2 <= 1.65
|   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |--- feature_2 >  1.65
|   |   |   |   |   |   |   |--- feature_1 <= 3.60
|   |   |   |   |   |   |   |   |--- value: [0.20]
|   |   |   |   |   |   |   |--- feature_1 >  3.60
|   |   |   |   |   |   |   |   |--- feature_0 <= 5.55
|   |   |   |   |   |   |   |   |   |--- value: [0.40]
|   |   |   |   |   |   |   |   |--- feature_0 >  5.55
|   |   |   |   |   |   |   |   |   |--- value: [0.30]
|--- feature_2 >  2.45
|   |--- feature_2 <= 4.75
|   |   |--- feature_2 <= 4.15
|   |   |   |--- feature_1 <= 2.65
|   |   |   |   |--- feature_2 <= 3.95
|   |   |   |   |   |--- feature_2 <= 3.75
|   |   |   |   |   |   |--- feature_2 <= 3.15
|   |   |   |   |   |   |   |--- value: [1.10]
|   |   |   |   |   |   |--- feature_2 >  3.15
|   |   |   |   |   |   |   |--- value: [1.00]
|   |   |   |   |   |--- feature_2 >  3.75
|   |   |   |   |   |   |--- feature_0 <= 5.55
|   |   |   |   |   |   |   |--- value: [1.10]
|   |   |   |   |   |   |--- feature_0 >  5.55
|   |   |   |   |   |   |   |--- value: [1.10]
|   |   |   |   |--- feature_2 >  3.95
|   |   |   |   |   |--- feature_0 <= 5.90
|   |   |   |   |   |   |--- feature_0 <= 5.65
|   |   |   |   |   |   |   |--- feature_1 <= 2.40
|   |   |   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |   |   |--- feature_1 >  2.40
|   |   |   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |   |--- feature_0 >  5.65
|   |   |   |   |   |   |   |--- value: [1.20]
|   |   |   |   |   |--- feature_0 >  5.90
|   |   |   |   |   |   |--- value: [1.00]
|   |   |   |--- feature_1 >  2.65
|   |   |   |   |--- feature_0 <= 5.75
|   |   |   |   |   |--- feature_0 <= 5.40
|   |   |   |   |   |   |--- value: [1.40]
|   |   |   |   |   |--- feature_0 >  5.40
|   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |--- feature_0 >  5.75
|   |   |   |   |   |--- feature_2 <= 4.05
|   |   |   |   |   |   |--- feature_2 <= 3.95
|   |   |   |   |   |   |   |--- value: [1.20]
|   |   |   |   |   |   |--- feature_2 >  3.95
|   |   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |--- feature_2 >  4.05
|   |   |   |   |   |   |--- value: [1.00]
|   |   |--- feature_2 >  4.15
|   |   |   |--- feature_2 <= 4.45
|   |   |   |   |--- feature_0 <= 5.80
|   |   |   |   |   |--- feature_1 <= 2.65
|   |   |   |   |   |   |--- value: [1.20]
|   |   |   |   |   |--- feature_1 >  2.65
|   |   |   |   |   |   |--- feature_1 <= 2.95
|   |   |   |   |   |   |   |--- feature_1 <= 2.80
|   |   |   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |   |   |--- feature_1 >  2.80
|   |   |   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |   |--- feature_1 >  2.95
|   |   |   |   |   |   |   |--- value: [1.20]
|   |   |   |   |--- feature_0 >  5.80
|   |   |   |   |   |--- feature_1 <= 2.95
|   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |--- feature_1 >  2.95
|   |   |   |   |   |   |--- feature_0 <= 6.25
|   |   |   |   |   |   |   |--- value: [1.50]
|   |   |   |   |   |   |--- feature_0 >  6.25
|   |   |   |   |   |   |   |--- value: [1.40]
|   |   |   |--- feature_2 >  4.45
|   |   |   |   |--- feature_0 <= 5.15
|   |   |   |   |   |--- value: [1.70]
|   |   |   |   |--- feature_0 >  5.15
|   |   |   |   |   |--- feature_1 <= 3.25
|   |   |   |   |   |   |--- feature_1 <= 2.95
|   |   |   |   |   |   |   |--- feature_2 <= 4.65
|   |   |   |   |   |   |   |   |--- feature_0 <= 5.85
|   |   |   |   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |   |   |   |--- feature_0 >  5.85
|   |   |   |   |   |   |   |   |   |--- feature_0 <= 6.55
|   |   |   |   |   |   |   |   |   |   |--- value: [1.50]
|   |   |   |   |   |   |   |   |   |--- feature_0 >  6.55
|   |   |   |   |   |   |   |   |   |   |--- value: [1.30]
|   |   |   |   |   |   |   |--- feature_2 >  4.65
|   |   |   |   |   |   |   |   |--- feature_1 <= 2.85
|   |   |   |   |   |   |   |   |   |--- value: [1.20]
|   |   |   |   |   |   |   |   |--- feature_1 >  2.85
|   |   |   |   |   |   |   |   |   |--- value: [1.40]
|   |   |   |   |   |   |--- feature_1 >  2.95
|   |   |   |   |   |   |   |--- feature_2 <= 4.55
|   |   |   |   |   |   |   |   |--- value: [1.50]
|   |   |   |   |   |   |   |--- feature_2 >  4.55
|   |   |   |   |   |   |   |   |--- feature_2 <= 4.65
|   |   |   |   |   |   |   |   |   |--- value: [1.40]
|   |   |   |   |   |   |   |   |--- feature_2 >  4.65
|   |   |   |   |   |   |   |   |   |--- feature_1 <= 3.15
|   |   |   |   |   |   |   |   |   |   |--- value: [1.50]
|   |   |   |   |   |   |   |   |   |--- feature_1 >  3.15
|   |   |   |   |   |   |   |   |   |   |--- value: [1.40]
|   |   |   |   |   |--- feature_1 >  3.25
|   |   |   |   |   |   |--- value: [1.60]
|   |--- feature_2 >  4.75
|   |   |--- feature_2 <= 5.05
|   |   |   |--- feature_0 <= 6.75
|   |   |   |   |--- feature_0 <= 5.80
|   |   |   |   |   |--- value: [2.00]
|   |   |   |   |--- feature_0 >  5.80
|   |   |   |   |   |--- feature_1 <= 2.35
|   |   |   |   |   |   |--- value: [1.50]
|   |   |   |   |   |--- feature_1 >  2.35
|   |   |   |   |   |   |--- feature_0 <= 6.25
|   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |   |   |--- feature_0 >  6.25
|   |   |   |   |   |   |   |--- feature_2 <= 4.95
|   |   |   |   |   |   |   |   |--- feature_1 <= 2.60
|   |   |   |   |   |   |   |   |   |--- value: [1.50]
|   |   |   |   |   |   |   |   |--- feature_1 >  2.60
|   |   |   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |   |   |   |--- feature_2 >  4.95
|   |   |   |   |   |   |   |   |--- feature_0 <= 6.50
|   |   |   |   |   |   |   |   |   |--- value: [1.90]
|   |   |   |   |   |   |   |   |--- feature_0 >  6.50
|   |   |   |   |   |   |   |   |   |--- value: [1.70]
|   |   |   |--- feature_0 >  6.75
|   |   |   |   |--- feature_0 <= 6.85
|   |   |   |   |   |--- value: [1.40]
|   |   |   |   |--- feature_0 >  6.85
|   |   |   |   |   |--- value: [1.50]
|   |   |--- feature_2 >  5.05
|   |   |   |--- feature_1 <= 3.05
|   |   |   |   |--- feature_0 <= 6.35
|   |   |   |   |   |--- feature_0 <= 5.85
|   |   |   |   |   |   |--- feature_1 <= 2.75
|   |   |   |   |   |   |   |--- value: [1.90]
|   |   |   |   |   |   |--- feature_1 >  2.75
|   |   |   |   |   |   |   |--- value: [2.40]
|   |   |   |   |   |--- feature_0 >  5.85
|   |   |   |   |   |   |--- feature_1 <= 2.85
|   |   |   |   |   |   |   |--- feature_1 <= 2.65
|   |   |   |   |   |   |   |   |--- value: [1.40]
|   |   |   |   |   |   |   |--- feature_1 >  2.65
|   |   |   |   |   |   |   |   |--- feature_1 <= 2.75
|   |   |   |   |   |   |   |   |   |--- value: [1.60]
|   |   |   |   |   |   |   |   |--- feature_1 >  2.75
|   |   |   |   |   |   |   |   |   |--- value: [1.50]
|   |   |   |   |   |   |--- feature_1 >  2.85
|   |   |   |   |   |   |   |--- feature_1 <= 2.95
|   |   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |   |   |   |--- feature_1 >  2.95
|   |   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |--- feature_0 >  6.35
|   |   |   |   |   |--- feature_0 <= 7.50
|   |   |   |   |   |   |--- feature_0 <= 7.15
|   |   |   |   |   |   |   |--- feature_1 <= 2.75
|   |   |   |   |   |   |   |   |--- feature_0 <= 6.55
|   |   |   |   |   |   |   |   |   |--- value: [1.90]
|   |   |   |   |   |   |   |   |--- feature_0 >  6.55
|   |   |   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |   |   |   |--- feature_1 >  2.75
|   |   |   |   |   |   |   |   |--- feature_0 <= 6.60
|   |   |   |   |   |   |   |   |   |--- feature_2 <= 5.55
|   |   |   |   |   |   |   |   |   |   |--- feature_2 <= 5.35
|   |   |   |   |   |   |   |   |   |   |   |--- value: [2.00]
|   |   |   |   |   |   |   |   |   |   |--- feature_2 >  5.35
|   |   |   |   |   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |   |   |   |   |   |--- feature_2 >  5.55
|   |   |   |   |   |   |   |   |   |   |--- feature_2 <= 5.70
|   |   |   |   |   |   |   |   |   |   |   |--- value: [2.15]
|   |   |   |   |   |   |   |   |   |   |--- feature_2 >  5.70
|   |   |   |   |   |   |   |   |   |   |   |--- value: [2.20]
|   |   |   |   |   |   |   |   |--- feature_0 >  6.60
|   |   |   |   |   |   |   |   |   |--- feature_0 <= 6.75
|   |   |   |   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |   |   |   |   |   |   |--- feature_0 >  6.75
|   |   |   |   |   |   |   |   |   |   |--- value: [2.10]
|   |   |   |   |   |   |--- feature_0 >  7.15
|   |   |   |   |   |   |   |--- feature_2 <= 5.95
|   |   |   |   |   |   |   |   |--- value: [1.60]
|   |   |   |   |   |   |   |--- feature_2 >  5.95
|   |   |   |   |   |   |   |   |--- feature_1 <= 2.85
|   |   |   |   |   |   |   |   |   |--- value: [1.90]
|   |   |   |   |   |   |   |   |--- feature_1 >  2.85
|   |   |   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |   |--- feature_0 >  7.50
|   |   |   |   |   |   |--- feature_2 <= 6.80
|   |   |   |   |   |   |   |--- feature_2 <= 6.35
|   |   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |   |   |   |   |--- feature_2 >  6.35
|   |   |   |   |   |   |   |   |--- feature_1 <= 2.90
|   |   |   |   |   |   |   |   |   |--- value: [2.00]
|   |   |   |   |   |   |   |   |--- feature_1 >  2.90
|   |   |   |   |   |   |   |   |   |--- value: [2.10]
|   |   |   |   |   |   |--- feature_2 >  6.80
|   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |--- feature_1 >  3.05
|   |   |   |   |--- feature_1 <= 3.25
|   |   |   |   |   |--- feature_2 <= 5.95
|   |   |   |   |   |   |--- feature_0 <= 6.60
|   |   |   |   |   |   |   |--- feature_2 <= 5.40
|   |   |   |   |   |   |   |   |--- feature_0 <= 6.45
|   |   |   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |   |   |   |   |   |--- feature_0 >  6.45
|   |   |   |   |   |   |   |   |   |--- value: [2.00]
|   |   |   |   |   |   |   |--- feature_2 >  5.40
|   |   |   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |   |   |--- feature_0 >  6.60
|   |   |   |   |   |   |   |--- feature_2 <= 5.50
|   |   |   |   |   |   |   |   |--- feature_2 <= 5.25
|   |   |   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |   |   |   |   |   |--- feature_2 >  5.25
|   |   |   |   |   |   |   |   |   |--- value: [2.10]
|   |   |   |   |   |   |   |--- feature_2 >  5.50
|   |   |   |   |   |   |   |   |--- feature_2 <= 5.65
|   |   |   |   |   |   |   |   |   |--- value: [2.40]
|   |   |   |   |   |   |   |   |--- feature_2 >  5.65
|   |   |   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |   |   |--- feature_2 >  5.95
|   |   |   |   |   |   |--- value: [1.80]
|   |   |   |   |--- feature_1 >  3.25
|   |   |   |   |   |--- feature_0 <= 7.45
|   |   |   |   |   |   |--- feature_2 <= 5.85
|   |   |   |   |   |   |   |--- feature_2 <= 5.65
|   |   |   |   |   |   |   |   |--- feature_2 <= 5.50
|   |   |   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |   |   |   |   |   |--- feature_2 >  5.50
|   |   |   |   |   |   |   |   |   |--- value: [2.40]
|   |   |   |   |   |   |   |--- feature_2 >  5.65
|   |   |   |   |   |   |   |   |--- value: [2.30]
|   |   |   |   |   |   |--- feature_2 >  5.85
|   |   |   |   |   |   |   |--- feature_0 <= 6.75
|   |   |   |   |   |   |   |   |--- value: [2.50]
|   |   |   |   |   |   |   |--- feature_0 >  6.75
|   |   |   |   |   |   |   |   |--- value: [2.50]
|   |   |   |   |   |--- feature_0 >  7.45
|   |   |   |   |   |   |--- feature_0 <= 7.80
|   |   |   |   |   |   |   |--- value: [2.20]
|   |   |   |   |   |   |--- feature_0 >  7.80
|   |   |   |   |   |   |   |--- value: [2.00]

​

树图绘制

python 复制代码 
from sklearn.tree import export_graphviz
import graphviz

#设置字体
from pylab import mpl
mpl.rcParams["font.sans-serif"] = ["SimHei"]  # 显示中文

# 使用export_graphviz生成DOT文件
dot_data = export_graphviz(model, out_file=None, 
                           feature_names=['花萼-width', '花萼-length', '花瓣-width'],  
                           class_names=['花瓣-length'],
                           filled=True, rounded=True,
                           special_characters=True) 

# 使用graphviz渲染DOT文件
graph = graphviz.Source(dot_data)
graph.render("decision_tree") # 将图形保存为PDF或其它格式
graph.view() # 在默认查看器中打开图形

图太长了，不方便展示，可以运行代码绘制。

ue: [2.50]

| | | | | | | |--- feature_0 > 6.75

| | | | | | | | |--- value: [2.50]

| | | | | |--- feature_0 > 7.45

| | | | | | |--- feature_0 <= 7.80

| | | | | | | |--- value: [2.20]

| | | | | | |--- feature_0 > 7.80

| | | | | | | |--- value: [2.00]

​    

## 树图绘制

```python
from sklearn.tree import export_graphviz
import graphviz

#设置字体
from pylab import mpl
mpl.rcParams["font.sans-serif"] = ["SimHei"]  # 显示中文

# 使用export_graphviz生成DOT文件
dot_data = export_graphviz(model, out_file=None, 
                           feature_names=['花萼-width', '花萼-length', '花瓣-width'],  
                           class_names=['花瓣-length'],
                           filled=True, rounded=True,
                           special_characters=True) 

# 使用graphviz渲染DOT文件
graph = graphviz.Source(dot_data)
graph.render("decision_tree") # 将图形保存为PDF或其它格式
graph.view() # 在默认查看器中打开图形

图太长了，不方便展示，可以运行代码绘制。

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