实验四 决策树算法及应用

作业信息

博客班级 https://edu.cnblogs.com/campus/ahgc/machinelearning
作业要求 https://edu.cnblogs.com/campus/ahgc/machinelearning/homework/12086
作业目标 理解决策树算法原理,掌握其实现方法并解决实际问题
学号 <3180701337>

一、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。

二、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。

三、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;

四、代码实现及注释

1.代码注释

(1)

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

(2)

# 书上题目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

(3)

datasets, labels = create_data()

(4)

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

(5)

train_data

(6)

# 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]])

(7)

info_gain_train(np.array(datasets))

(8)

# 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)

(9)

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)

pip install graphviz

(14)

from sklearn.tree import DecisionTreeClassifier
from sklearn.tree import export_graphviz
import graphviz

(15)

clf = DecisionTreeClassifier()
clf.fit(X_train, y_train,)

(16)

clf.score(X_test, y_test)

(17)

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

(18)

graphviz.Source(dot_graph)

(19)

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

(20)

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

2.运行结果

3.讨论ID3、5算法的应用场景

ID3算法的应用场景:ID3 算法的核心思想就是以信息增益来度量特征选择,选择信息增益最大的特征进行分裂。缺点是:
1.ID3 没有剪枝策略,容易过拟合;
2.信息增益准则对可取值数目较多的特征有所偏好,类似“编号”的特征其信息增益接近于 1;
3.只能用于处理离散分布的特征;
4.没有考虑缺失值。
所以ID3的应用对于有离散特征的问题来说更好,在机器学习、知识发现和数据挖掘等领域有很好体现。

C4.5算法的应用场景:C4.5 算法最大的特点是克服了 ID3 对特征数目的偏重这一缺点,引入信息增益率来作为分类标准。缺点是:
1.C4.5 用的是多叉树,用二叉树效率更高;
2.C4.5只能用于分类问题中;
3.C4.5 使用的熵模型拥有大量耗时的对数运算,连续值还有排序运算;
4.C4.5 在构造树的过程中,对数值属性值需要按照其大小进行排序,从中选择一个分割点,所以只适合于能够驻留于内存的数据集,当训练集大得无法在内存容纳时,程序无法运行。
C4.5相对于ID3算法来说更好,但其只能用于分类问题中。在机器学习、知识发现、金融分析、遥感影像分类等问题中得到了较为广泛的应用。

五、实验小结

通过本次实验,我对决策树的原理和相关知识有了更多的认识,并且由于在实现中未安装graphviz相关的包而导致在绘图过程中遇到了很多的问题,最后还是查阅了相关资料解决了
该问题,完成了实验报告的撰写,在实验过程中我对决策树算法也有了更多的认识。

参考文献:https://blog.csdn.net/lizzy05/article/details/88529483

posted on 2021-06-30 22:14  outlier7  阅读(80)  评论(0编辑  收藏  举报