实验四决策树算法及应用

作业信息

个人班级	机器学习实验-计算机18级
实验题目	实验四决策树算法及应用
姓名	马腾宇
学号	3180701202

实验目的

1.理解决策树算法原理，掌握决策树算法框架；
2.理解决策树学习算法的特征选择、树的生成和树的剪枝；
3.能根据不同的数据类型，选择不同的决策树算法；
4.针对特定应用场景及数据，能应用决策树算法解决实际问题。

实验内容

1.设计算法实现熵、经验条件熵、信息增益等方法。
2.实现ID3算法。
3.熟悉sklearn库中的决策树算法；
4.针对iris数据集，应用sklearn的决策树算法进行类别预测。
5.针对iris数据集，利用自编决策树算法进行类别预测。

实验报告要求

1.对照实验内容，撰写实验过程、算法及测试结果；
2.代码规范化：命名规则、注释；
3.分析核心算法的复杂度；
4.查阅文献，讨论ID3、5算法的应用场景；
查询文献，分析决策树剪枝策略。

实验代码

import numpy as np

import pandas as pd

import matplotlib.pyplot as plt

%matplotlib inline

from sklearn.datasets import load_iris

from sklearn.model_selection import train_test_split

from collections import Counter

import math

from math import log

import pprint

def create_data():

datasets = [['青年', '否', '否', '一般', '否'],

['青年', '否', '否', '好', '否'],

['青年', '是', '否', '好', '是'],

['青年', '是', '是', '一般', '是'],

['青年', '否', '否', '一般', '否'],

['中年', '否', '否', '一般', '否'],

['中年', '否', '否', '好', '否'],

['中年', '是', '是', '好', '是'],

['中年', '否', '是', '非常好', '是'],

['中年', '否', '是', '非常好', '是'],

['老年', '否', '是', '非常好', '是'],

['老年', '否', '是', '好', '是'],

['老年', '是', '否', '好', '是'],

['老年', '是', '否', '非常好', '是'],

['老年', '否', '否', '一般', '否'],

]

labels = [u'年龄', u'有工作', u'有自己的房子', u'信贷情况', u'类别']

# 返回数据集和每个维度的名称

return datasets, labels

datasets, labels = create_data()

train_data = pd.DataFrame(datasets, columns=labels)

train_data

# 熵

def calc_ent(datasets):

data_length = len(datasets)

label_count = {}

for i in range(data_length):

label = datasets[i][-1]

if label not in label_count:

label_count[label] = 0

label_count[label] += 1

ent = -sum([(p / data_length) * log(p / data_length, 2)

for p in label_count.values()])

return ent

# def entropy(y):

# """

# Entropy of a label sequence

# """

# hist = np.bincount(y)

# ps = hist / np.sum(hist)

# return -np.sum([p * np.log2(p) for p in ps if p > 0])

# 经验条件熵

def cond_ent(datasets, axis=0):

data_length = len(datasets)

feature_sets = {}

for i in range(data_length):

feature = datasets[i][axis]

if feature not in feature_sets:

feature_sets[feature] = []

feature_sets[feature].append(datasets[i])

cond_ent = sum(

[(len(p) / data_length) * calc_ent(p) for p in feature_sets.values()])

return cond_ent

# 信息增益

def info_gain(ent, cond_ent):

return ent - cond_ent

def info_gain_train(datasets):

count = len(datasets[0]) - 1

ent = calc_ent(datasets)

# ent = entropy(datasets)

best_feature = []

for c in range(count):

c_info_gain = info_gain(ent, cond_ent(datasets, axis=c))

best_feature.append((c, c_info_gain))

print('特征({}) - info_gain - {:.3f}'.format(labels[c], c_info_gain))

# 比较大小

best_ = max(best_feature, key=lambda x: x[-1])

return '特征({})的信息增益最大，选择为根节点特征'.format(labels[best_[0]])

info_gain_train(np.array(datasets))

# 定义节点类 二叉树

class Node:

def init(self, root=True, label=None, feature_name=None, feature=None):

self.root = root

self.label = label

self.feature_name = feature_name

self.feature = feature

self.tree = {}

self.result = {

'label:': self.label,

'feature': self.feature,

'tree': self.tree

}

def repr(self):

return '{}'.format(self.result)

def add_node(self, val, node):

self.tree[val] = node

def predict(self, features):

if self.root is True:

return self.label

return self.tree[features[self.feature]].predict(features)

class DTree:

def init(self, epsilon=0.1):

self.epsilon = epsilon

self.tree = {}

# 熵

@staticmethod

def calc_ent(datasets):

data_length = len(datasets)

label_count = {}

for i in range(data_length):

label = datasets[i][-1]

if label not in label_count:

label_count[label] = 0

label_count[label] += 1

ent = -sum([(p / data_length) * log(p / data_length, 2)

for p in label_count.values()])

return ent

# 经验条件熵

def cond_ent(self, datasets, axis=0):

data_length = len(datasets)

feature_sets = {}

for i in range(data_length):

feature = datasets[i][axis]

if feature not in feature_sets:

feature_sets[feature] = []

feature_sets[feature].append(datasets[i])

cond_ent = sum([(len(p) / data_length) * self.calc_ent(p)

for p in feature_sets.values()])

return cond_ent

# 信息增益

@staticmethod

def info_gain(ent, cond_ent):

return ent - cond_ent

def info_gain_train(self, datasets):

count = len(datasets[0]) - 1

ent = self.calc_ent(datasets)

best_feature = []

for c in range(count):

c_info_gain = self.info_gain(ent, self.cond_ent(datasets, axis=c))

best_feature.append((c, c_info_gain))

# 比较大小

best = max(best_feature, key=lambda x: x[-1])

return best_

def train(self, train_data):

"""

input:数据集D(DataFrame格式)，特征集A，阈值eta

output:决策树T

"""

_, y_train, features = train_data.iloc[:, :

-1], train_data.iloc[:,

-1], train_data.columns[:

-1]

# 1,若D中实例属于同一类Ck，则T为单节点树，并将类Ck作为结点的类标记，返回T

if len(y_train.value_counts()) == 1:

return Node(root=True, label=y_train.iloc[0])

# 2, 若A为空，则T为单节点树，将D中实例树最大的类Ck作为该节点的类标记，返回T

if len(features) == 0:

return Node(

root=True,

label=y_train.value_counts().sort_values(

ascending=False).index[0])

# 3,计算最大信息增益 同5.1,Ag为信息增益最大的特征

max_feature, max_info_gain = self.info_gain_train(np.array(train_data))

max_feature_name = features[max_feature]

# 4,Ag的信息增益小于阈值eta,则置T为单节点树，并将D中是实例数最大的类Ck作为该节点的类标记，返

if max_info_gain < self.epsilon:

return Node(

root=True,

label=y_train.value_counts().sort_values(

ascending=False).index[0])

# 5,构建Ag子集

node_tree = Node(

root=False, feature_name=max_feature_name, feature=max_feature)

feature_list = train_data[max_feature_name].value_counts().index

for f in feature_list:

sub_train_df = train_data.loc[train_data[max_feature_name] ==

f].drop([max_feature_name], axis=1)

# 6, 递归生成树

sub_tree = self.train(sub_train_df)

node_tree.add_node(f, sub_tree)

# pprint.pprint(node_tree.tree)

return node_tree

def fit(self, train_data):

self._tree = self.train(train_data)

return self._tree

def predict(self, X_test):

return self._tree.predict(X_test)

datasets, labels = create_data()

data_df = pd.DataFrame(datasets, columns=labels)

dt = DTree()

tree = dt.fit(data_df)

10.

tree

11.

dt.predict(['老年', '否', '否', '一般'])

12.

# data

def create_data():

iris = load_iris()

df = pd.DataFrame(iris.data, columns=iris.feature_names)

df['label'] = iris.target

df.columns = [

'sepal length', 'sepal width', 'petal length', 'petal width', 'label'

]

data = np.array(df.iloc[:100, [0, 1, -1]])

# print(data)

return data[:, :2], data[:, -1]

X, y = create_data()

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3)

13.

from sklearn.tree import DecisionTreeClassifier

from sklearn.tree import export_graphviz

import graphviz

14.

clf = DecisionTreeClassifier()

clf.fit(X_train, y_train,)

15.

clf.score(X_test, y_test)

16.

tree_pic = export_graphviz(clf, out_file="mytree.pdf")

with open('mytree.pdf') as f:

dot_graph = f.read()

17.

graphviz.Source(dot_graph)

18.

from sklearn.tree import DecisionTreeClassifier

from sklearn import preprocessing

import numpy as np

import pandas as pd

from sklearn import tree

import graphviz

features = ["年龄", "有工作", "有自己的房子", "信贷情况"]

X_train = pd.DataFrame([

["青年", "否", "否", "一般"],

["青年", "否", "否", "好"],

["青年", "是", "否", "好"],

["青年", "是", "是", "一般"],

["青年", "否", "否", "一般"],

["中年", "否", "否", "一般"],

["中年", "否", "否", "好"],

["中年", "是", "是", "好"],

["中年", "否", "是", "非常好"],

["中年", "否", "是", "非常好"],

["老年", "否", "是", "非常好"],

["老年", "否", "是", "好"],

["老年", "是", "否", "好"],

["老年", "是", "否", "非常好"],

["老年", "否", "否", "一般"]

])

y_train = pd.DataFrame(["否", "否", "是", "是", "否",

"否", "否", "是", "是", "是",

"是", "是", "是", "是", "否"])

# 数据预处理

le_x = preprocessing.LabelEncoder()

le_x.fit(np.unique(X_train))

X_train = X_train.apply(le_x.transform)

le_y = preprocessing.LabelEncoder()

le_y.fit(np.unique(y_train))

y_train = y_train.apply(le_y.transform)

# 调用sklearn.DT建立训练模型

model_tree = DecisionTreeClassifier()

model_tree.fit(X_train, y_train)

# 可视化

dot_data = tree.export_graphviz(model_tree, out_file=None,

feature_names=features,

class_names=[str(k) for k in np.unique(y_train)],

filled=True, rounded=True,

special_characters=True)

graph = graphviz.Source(dot_data)

graph

19.

import numpy as np

class LeastSqRTree:

def init(self, train_X, y, epsilon):

# 训练集特征值

self.x = train_X

# 类别

self.y = y

# 特征总数

self.feature_count = train_X.shape[1]

# 损失阈值

self.epsilon = epsilon

# 回归树

self.tree = None

def _fit(self, x, y, feature_count, epsilon):

# 选择最优切分点变量j与切分点s

(j, s, minval, c1, c2) = self._divide(x, y, feature_count)

# 初始化树

tree = {"feature": j, "value": x[s, j], "left": None, "right": None}

if minval < self.epsilon or len(y[np.where(x[:, j] <= x[s, j])]) <= 1:

tree["left"] = c1

else:

tree["left"] = self._fit(x[np.where(x[:, j] <= x[s, j])],

y[np.where(x[:, j] <= x[s, j])],

self.feature_count, self.epsilon)

if minval < self.epsilon or len(y[np.where(x[:, j] > s)]) <= 1:

tree["right"] = c2

else:

tree["right"] = self._fit(x[np.where(x[:, j] > x[s, j])],

y[np.where(x[:, j] > x[s, j])],

self.feature_count, self.epsilon)

return tree

def fit(self):

self.tree = self._fit(self.x, self.y, self.feature_count, self.epsilon)

@staticmethod

def _divide(x, y, feature_count):

# 初始化损失误差

cost = np.zeros((feature_count, len(x)))

# 公式5.21

for i in range(feature_count):

for k in range(len(x)):

# k行i列的特征值

value = x[k, i]

y1 = y[np.where(x[:, i] <= value)]

c1 = np.mean(y1)

y2 = y[np.where(x[:, i] > value)]

c2 = np.mean(y2)

y1[:] = y1[:] - c1

y2[:] = y2[:] - c2

cost[i, k] = np.sum(y1 * y1) + np.sum(y2 * y2)

# 选取最优损失误差点

cost_index = np.where(cost == np.min(cost))

# 选取第几个特征值

j = cost_index[0][0]

# 选取特征值的切分点

s = cost_index[1][0]

# 求两个区域的均值c1,c2

c1 = np.mean(y[np.where(x[:, j] <= x[s, j])])

c2 = np.mean(y[np.where(x[:, j] > x[s, j])])

return j, s, cost[cost_index], c1, c2

20.

train_X = np.array([[1, 2, 3, 4, 5, 6, 7, 8, 9, 10]]).T

y = np.array([4.50, 4.75, 4.91, 5.34, 5.80, 7.05, 7.90, 8.23, 8.70, 9.00])

model_tree = LeastSqRTree(train_X, y, .2)

model_tree.fit()

model_tree.tree