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。
【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。
【实验过程】
1.导入包
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.创建相对应数据
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.
datasets,labels=create_data()
4.
train_data=pd.DataFrame(datasets,columns=labels)
5.
train_data
6.设计算法实现熵、经验条件熵、信息增益
# 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 #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) 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.针对给定的房贷数据集(数据集表格见附录1)实现ID3算法
# 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)
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tree
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dt.predict(['老年', '否', '否', '一般'])
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# 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.熟悉sklearn库中的决策树算法
from sklearn.tree import DecisionTreeClassifier from sklearn.tree import export_graphviz import graphviz
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clf = DecisionTreeClassifier()
clf.fit(X_train, y_train,)
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clf.score(X_test, y_test)
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tree_pic = export_graphviz(clf, out_file="mytree.pdf")
with open('mytree.pdf') as f:
dot_graph = f.read()
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graphviz.Source(dot_graph)
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
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
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
【实验中遇到的问题】
实验中还需要安装graphviz，更改环境变量配置。
【实验小结】
D3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。
决策树算法的优点：
1）简单直观，生成的决策树很直观。
2）基本不需要预处理，不需要提前归一化，处理缺失值。
3）使用决策树预测的代价是O(log2m)。
4）既可以处理离散值也可以处理连续值。很多算法只是专注于离散值或者连续值。
5）可以处理多维度输出的分类问题。
6）相比于神经网络之类的黑盒分类模型，决策树在逻辑上可以得到很好的解释。
7）可以交叉验证的剪枝来选择模型，从而提高泛化能力。
8） 对于异常点的容错能力好，健壮性高。
决策树算法的缺点:
1）决策树算法非常容易过拟合，导致泛化能力不强。可以通过设置节点最少样本数量和限制决策树深度来改进。
2）决策树会因为样本发生一点点的改动，就会导致树结构的剧烈改变。这个可以通过集成学习之类的方法解决。
3）寻找最优的决策树是一个NP难的问题，我们一般是通过启发式方法，容易陷入局部最优。可以通过集成学习之类的方法来改善。
4）有些比较复杂的关系，决策树很难学习，比如异或。一般这种关系可以换神经网络分类方法来解决。
5）如果某些特征的样本比例过大，生成决策树容易偏向于这些特征。这个可以通过调节样本权重来改善。
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