实验一：决策树算法实验
实验一：决策树算法实验
【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。
- 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。
- 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；
- 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。
【实验步骤与结果】
实验代码
1.导包
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.导入数据
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'] #返回数据和每个维度的名称 return datasets,labels
3.数据集转为DataFrame表格
datasets,labels=create_data() train_data=pd.DataFrame(datasets,columns=labels) train_data
4.计算数据集的熵，经验条件熵，信息增益
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)
5.创建决策树
datasets, labels = create_data() data_df = pd.DataFrame(datasets, columns=labels) dt = DTree() tree = dt.fit(data_df) tree
输出
dt.predict(['老年', '否', '否', '一般'])
6.应用sklearrn决策树算法对iris数据集进行类别预测
from sklearn.tree import DecisionTreeClassifier from sklearn.tree import export_graphviz import graphviz # 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) 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)
7.
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"]) 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) model_tree = DecisionTreeClassifier() model_tree.fit(X_train, y_train) 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
【实验小结】
-
ID3算法的应用场景：
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。
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C4.5算法的应用场景：
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。
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决策树基本策略：
预剪枝：在决策树生成过程中，对每个节点在划分之前先进行估计，若当前节点的划分不能带来决策树泛化性能的提升，则停止划分，并将当前节点标记为叶节点。
后剪枝：先从训练集中生成一课完整的决策树，然后自底向上对非叶子节点进行考察，若将该节点对应的子树替换为叶子结点能带来决策树泛化性能的提升，则将该子树替换为叶节点。
4.需安装graphviz，更改环境变量配置并在 Jupyter notebook中导入graphviz使图形显示
