实验四 决策树算法及应用


博客班级 机器学习
作业要求 实验四 决策树算法及应用
作业目标 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。
学号 3180701211

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.实验代码

1.设计算法实现熵、经验条件熵、信息增益等方法

In [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

In [2]:

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

In [3]:

datasets, labels = create_data()

In [4]:

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

In [5]:

train_data

In [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]])

2.实现ID3算法


In [7]:

info_gain_train(np.array(datasets))

In [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
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)

3.针对iris数据集,应用sklearn的决策树算法进行类别预测

In [9]:

datasets, labels = create_data()
data_df = pd.DataFrame(datasets, columns=labels)
dt = DTree()
tree = dt.fit(data_df)

In [10]:

tree

In [11]:

dt.predict(['老年', '否', '否', '一般'])

In [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)

In [13]:

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

In [14]:

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

In [15]:

clf.score(X_test, y_test)


In [16]:

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

In [17]:

graphviz.Source(dot_graph

In [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

In [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

In [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

五.思考题

讨论ID3、5算法的应用场景

ID3算法应用场景:
它的基础理论清晰,算法比较简单,学习能力较强,适于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算法应用场景:
C4.5算法具有条理清晰,能处理连续型属性,防止过拟合,准确率较高和适用范围广等优点,是一个很有实用价值的决策树算法,可以用来分类,也可以用来回归。C4.5算法在机器学习、知识发现、金融分析、遥感影像分类、生产制造、分子生物学和数据挖掘等领域得到广泛应用。

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。
优点: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。
缺点: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;
预剪枝基于'贪心'本质禁止这些分支展开,给预剪枝决策树带来了欠拟合的风险。
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。
优点:一般情况下后剪枝决策树的欠拟合风险很小,泛化性能往往优于预剪枝决策树。
缺点:自底向上的注意考察,时间开销较高。

六.实验小结

本次实验理解了决策树算法原理(在决策树学习中,ID3(Iterative Dichotomiser 3)是一种由Ross Quinlan发明的用来从数据集中生成决策树的算法。ID3是C4.5算法的前身,其常用于机器学习和自然语言处理领域。D3算法将初始集合S作为根节点,在算法的每一步迭代中,其遍历集合中的每个为使用的属性,计算该属性的熵或信息增益。从中选择具有最小熵H(S)或最大信息增益IG(A)的属性。再用选定的属性将集合S分为不同的数据子集。算法继续对每个子集进行递归处理,每次只考虑之前没有选定的属性),掌握了决策树算法框架;并且学会了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。

posted @ 2021-06-30 19:06  李世媛  阅读(116)  评论(0编辑  收藏  举报