【个人信息】

【实验目的】

理解决策树算法原理，掌握决策树算法框架；
理解决策树学习算法的特征选择、树的生成和树的剪枝；
能根据不同的数据类型，选择不同的决策树算法；
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】

设计算法实现熵、经验条件熵、信息增益等方法。
实现ID3算法。
熟悉sklearn库中的决策树算法；
针对iris数据集，应用sklearn的决策树算法进行类别预测。
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】

对照实验内容，撰写实验过程、算法及测试结果；
代码规范化：命名规则、注释；
分析核心算法的复杂度；
查阅文献，讨论ID3、5算法的应用场景；
【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
例题5.1
、、、
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))
【运行截图】

例题5.3
、、、# 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)

tree
dt.predict(['老年', '否', '否', '一般'])
【运行截图】

scikit-learn实例
、、、

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)
from sklearn.tree import DecisionTreeClassifier
from sklearn.tree import export_graphviz
import graphviz
clf = DecisionTreeClassifier()
clf.fit(X_train, y_train,)
clf.score(X_test, y_test)
tree_pic = export_graphviz(clf, out_file="mytree.pdf")
with open('mytree.pdf') as f:
dot_graph = f.read()

graphviz.Source(dot_graph)
【运行截图】

实验小结
本次实验是关于决策树的算法的相关实验，使我进一步掌握了决策树算法的原理，对于sklearn第三库自带的决策树算法我也在本次实验中有了基本的了解并且学会了如何使用，其实决策树本质上是从训练数据集中归纳出一组分类规则。理解决策树算法原理，掌握决策树算法框架；理解决策树学习算法的特征选择、树的生成和树的剪枝；能根据不同的数据类型，选择不同的决策树算法；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。