1 决策树自编程实现
import numpy as np import pandas as pd import math import time from collections import namedtuple class Node(namedtuple("Node","children type content feature label")): # 孩子节点、分类特征的取值、节点内容、节点分类特征、标签 """定义节点""" def __repr__(self): return str(tuple(self)) class DecisionTree(): """决策树""" def __init__(self,method="info_gain_ratio"): self.tree=None self.method=method def _experienc_entropy(self,X): """计算经验熵""" # 统计每个取值的出现频率 x_types_prob=X.iloc[:,0].value_counts()/X.shape[0] # 计算经验熵 x_experienc_entropy=sum((-p*math.log(p,2) for p in x_types_prob)) return x_experienc_entropy def _conditinal_entropy(self,X_train,y_train,feature): """计算条件熵""" # feature特征下每个特征取值数量统计 x_types_count= X_train[feature].value_counts() # 每个特征取值频率计算 x_types_prob = x_types_count / X_train.shape[0] # 每个特征取值下类别y的经验熵 x_experienc_entropy=[self._experienc_entropy(y_train[(X_train[feature]==i).values]) for i in x_types_count.index] # 特征feature对数据集的经验条件熵 x_conditinal_entropy=(x_types_prob.mul(x_experienc_entropy)).sum() return x_conditinal_entropy def _information_gain(self,X_train,y_train,feature): """计算信息增益""" return self._experienc_entropy(y_train)-self._conditinal_entropy(X_train,y_train,feature) def _information_gain_ratio(self,X_train,y_train,features,feature): """计算信息增益比""" index=features.index(feature) return self._information_gain(X_train,y_train,feature)/self._experienc_entropy(X_train.iloc[:,index:index+1]) def _choose_feature(self,X_train,y_train,features): """选择分类特征""" if self.method=="info_gain_ratio": info=[self._information_gain_ratio(X_train,y_train,features,feature) for feature in features] elif self.method=="info_gain": info=[self._information_gain(X_train,y_train,feature) for feature in features] else: raise TypeError optimal_feature=features[np.argmax(info)] # for i in range(len(features)): # print(features[i],":",info[i]) return optimal_feature def _built_tree(self,X_train,y_train,features,type=None): """递归构造决策树""" # 只有一个节点或已经完全分类，则决策树停止继续分叉 if len(features)==1 or len(np.unique(y_train))==1: label=list(y_train[0].value_counts().index)[0] return Node(children=None,type=type,content=(X_train,y_train),feature=None,label=label) else: # 选择分类特征值 feature=self._choose_feature(X_train,y_train,features) features.remove(feature) # 构建节点，同时递归创建孩子节点 features_iter=np.unique(X_train[feature]) children=[] for item in features_iter: X_item=X_train[(X_train[feature]==item).values] y_item=y_train[(X_train[feature]==item).values] children.append(self._built_tree(X_item,y_item,features,type=item)) return Node(children=children,type=type,content=None,feature=feature,label=None) def _prune(self): """进行剪枝""" pass def fit(self,X_train,y_train,features): self.tree=self._built_tree(X_train,y_train,features) #self.tree=self._prune(tree) def _search(self,X_new): tree=self.tree # 若还有孩子节点，则继续向下搜索，否则搜索停止，在当前节点获取标签 while tree.children: for child in tree.children: if X_new[tree.feature].loc[0]==child.type: tree=child break return tree.label def predict(self,X_new): return self._search(X_new) def main(): star=time.time() # 训练数据集 features=["年龄","有工作","有自己的房子","信贷情况"] X_train=np.array([ ["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=np.array(["否","否","是", "是", "否", "否", "否", "是", "是", "是", "是", "是", "是", "是", "否"]) # 转换成pd.DataFrame模式 X_train = pd.DataFrame(X_train, columns=features) y_train = pd.DataFrame(y_train) # 训练 clf=DecisionTree(method="info_gain") clf.fit(X_train,y_train,features.copy()) # 预测 X_new=np.array([["青年", "是", "否", "一般"]]) X_new= pd.DataFrame(X_new, columns=features) y_predict=clf.predict(X_new) print(y_predict) print("time:{:.4f}s".format(time.time()-star)) if __name__=="__main__": main()
2 调用sklearn实现
from sklearn.tree import DecisionTreeClassifier from sklearn import preprocessing import numpy as np import pandas as pd import time from IPython.display import Image from sklearn import tree import pydotplus def show(clf,features,y_types): """决策树的可视化""" dot_data = tree.export_graphviz(clf, out_file=None, feature_names=features, class_names=y_types, filled=True, rounded=True, special_characters=True) graph = pydotplus.graph_from_dot_data(dot_data) #Image(graph.create_png()) #jupyter里可以显示，pycharm显示不出 graph.write_png(r'DT_show.png') def main(): star=time.time() # 原始样本数据 features=["age","work","house","credit"] 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) print(X_train) 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 clf=DecisionTreeClassifier() clf.fit(X_train,y_train) # 可视化 show(clf,features,[str(k) for k in np.unique(y_train)]) # 用训练得到模型进行预测 X_new=pd.DataFrame([["青年", "否", "是", "一般"]]) X=X_new.apply(le_x.transform) y_predict=clf.predict(X) # 结果输出 X_show=[{features[i]:X_new.values[0][i]} for i in range(len(features))] print("{0}被分类为:{1}".format(X_show,le_y.inverse_transform(y_predict))) print("time:{:.4f}s".format(time.time()-star)) if __name__=="__main__": main()
参考：
[1] 《统计学习方法》李航
[2] 深度之眼统计学习方法集训营课后练习（http://www.deepshare.net/）