决策树实验

#一、【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。
#二、【实验内容】

#设计算法实现熵、经验条件熵、信息增益等方法。
#针对给定的房贷数据集(数据集表格见附录1)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。
#三、【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；
#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。


#1决策树
import numpy as np
2 import pandas as pd    
3 from sklearn.datasets import load_iris    #数据模块
4 from sklearn.model_selection import train_test_split  #划分为训练集和测试集
5 from collections import Counter  #计数器
6 import math 
7 from math import log

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']
     
    return datasets, labels
     
datasets, labels = create_data()
 
train_data = pd.DataFrame(datasets, columns=labels)


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

信息熵

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

#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()])

calc_ent(datasets)

def info_gain(ent, cond_ent):
    return ent - cond_ent
def info_gain_train(datasets):
    count = len(datasets[0]) - 1
    ent = calc_ent(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({}) 的信息增益为： {:.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]])

1	`info_gain_train(np.array(datasets))`

IDE3算法

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，返回T
        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'])

决策树算法

from sklearn.datasets import load_iris
from sklearn.model_selection import train_test_split
from collections import Counter

# 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],iris.feature_names[0:2]
 
 
X, y,feature_name= 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
from sklearn import tree
 
clf = DecisionTreeClassifier()
clf.fit(X_train, y_train,)
 
clf.score(X_test, y_test)

tree.plot_tree(clf)

tree_pic = export_graphviz(clf, out_file="mytree.pdf")
with open('mytree.pdf') as f:
    dot_graph = f.read()
graphviz.Source(dot_graph)

IDE3算法应用场景

处理大规模的学习问题，是数据挖掘和知识发现领域中的一个很好的范例，为后来各学者提出优化算法奠定了理论基础。ID3算法特别在机器学习、知识发现和数据挖掘等领域得到了极大发展。

C4.5算法在机器学习数据挖掘有广泛用途

分析决策树剪枝策略

剪枝的目的在于：缓解决策树的"过拟合"，降低模型复杂度，提高模型整体的学习效率，决策树生成学习局部的模型，而决策树剪枝学习整体的模型

基本策略：

预剪枝：是指在决策树生成过程中，对每一个结点在划分前进行估计，若当前结点的划分不能带来决策树泛化性能提升，则停止划分并将当前结点标记为叶子结点。
降低了过拟合地风险，并显著减少了决策树地训练时间开销和测试时间开销。有些分支地当前划分虽不能提升泛化性能、甚至可能导致泛化性能下降，但是在其基础上进行地后续划分却可能导致性能显著提高；
后剪枝：先从训练集生成一棵完整的决策树，然后自底向上地对非叶子结点进行考察，若将该结点对应地子树替换为叶结点能带来决策树泛化性能提升，则将该子树替换为叶结点。