# -*- coding: utf-8 -*- ''' Created on 2018年1月15日 @author: Jason.F @summary: Scikit-Learn庫決策樹算法 '''from sklearn import datasets import numpy as np from sklearn.cross_validation import train_test_split from sklearn.preprocessing import StandardScaler from matplotlib.colors import ListedColormap import matplotlib.pyplot as plt from sklearn.svm import SVC from sklearn.metrics import accuracy_score from sklearn.tree import DecisionTreeClassifier from sklearn.tree import export_graphviz from sklearn.ensemble import RandomForestClassifier #決策邊界函數 def plot_decision_regions(X,y,classifier,test_idx=None,resolution=0.02):# 設置標記點和顏色markers = ('s','x','o','^','v')colors = ('red', 'blue', 'lightgreen', 'gray', 'cyan')cmap = ListedColormap(colors[:len(np.unique(y))])# 繪制決策面x1_min, x1_max = X[:, 0].min() - 1, X[:, 0].max() + 1x2_min, x2_max = X[:, 1].min() - 1, X[:, 1].max() + 1xx1, xx2 = np.meshgrid(np.arange(x1_min, x1_max, resolution),np.arange(x2_min, x2_max, resolution))Z = classifier.predict(np.array([xx1.ravel(), xx2.ravel()]).T)Z = Z.reshape(xx1.shape)plt.contourf(xx1, xx2, Z, alpha=0.4, cmap=cmap)plt.xlim(xx1.min(), xx1.max())plt.ylim(xx2.min(), xx2.max())#繪制所有樣本X_test,y_test=X[test_idx,:],y[test_idx]for idx,cl in enumerate(np.unique(y)):plt.scatter(x=X[y==cl,0],y=X[y==cl,1],alpha=0.8,c=cmap(idx),marker=markers[idx],label=cl)#高亮預測樣本if test_idx:X_test,y_test =X[test_idx,:],y[test_idx]plt.scatter(X_test[:,0],X_test[:,1],c='',alpha=1.0,linewidths=1,marker='o',s=55,label='test set') #數據導入 iris=datasets.load_iris() X=iris.data[:,[2,3]] y=iris.target print (np.unique(y)) #訓練集和測試集劃分 X_train,X_test,y_train,y_test=train_test_split(X,y,test_size=0.3,random_state=0) #標準化 sc=StandardScaler() sc.fit(X_train)#計算樣本的均值和標準差 X_train_std=sc.transform(X_train) X_test_std=sc.transform(X_test) #決策樹模型，信息增益和純度(熵、基尼系統、誤分類率) #深度越大，容易產生過擬合，通過剪枝來解決 tree=DecisionTreeClassifier(criterion='entropy',max_depth=3,random_state=0) tree.fit(X_train_std,y_train) #隨機森林，集成多個弱學習器成魯棒性強學習器 #參數：n_jobs處理器內核數量，n_estimators集成的單顆決策樹數量 #forest=RandomForestClassifier(criterion='entropy',n_estimators=10,n_jobs=2,random_state=1) #forest.fit(X_train_std,y_train) #模型預測 y_pred=tree.predict(X_test_std) print ('Accuracy:%.2f' %accuracy_score(y_test,y_pred))#準確率 #繪制決策邊界 X_combined_std=np.vstack((X_train_std,X_test_std)) y_combined=np.hstack((y_train,y_test)) plot_decision_regions(X=X_combined_std, y=y_combined, classifier=tree, test_idx=range(105,150)) plt.xlabel('petal length[cm]') plt.ylabel('petal width[cm]') plt.legend(loc='upper left') plt.show() #導出決策樹到dot格式 export_graphviz(tree,out_file='tree.dot',feature_names=['petal length','petal width']) #下載http://www.graphviz.org/download/ #dot轉換為png命令：dot -Tpng tree.dot -o tree.png #windows下安裝graphviz參考；http://blog.csdn.net/lanchunhui/article/details/49472949#觀察熵、基尼、誤分類率對純度的影響 def gini(p):return p*(1-p)+(1-p)*(1-(1-p)) def entropy(p):return -p*np.log2(p)-(1-p)*np.log2(1-p) def error(p):return 1-np.max([p,1-p]) x=np.arange(0.0,1.0,0.01) ent=[entropy(p) if p !=0 else None for p in x]#求熵 sc_ent=[e*0.5 if e else None for e in ent ]#熵縮放 err=[error(i) for i in x] fig=plt.figure() ax=plt.subplot(111) for i,lab,ls,c in zip([ent,sc_ent,gini(x),err],\['Entropy','Entropy(scaled)','Gini Impurity','Misclassification Error'],\['-','-','--','-.'],\['black','lightgray','red','green']):line=ax.plot(x,i,label=lab,linestyle=ls,lw=2,color=c) ax.legend(loc='upper center',bbox_to_anchor=(0.5,1.15),ncol=3,fancybox=True,shadow=False) ax.axhline(y=0.5,linewidth=1,color='k',linestyle='--') ax.axhline(y=1.0,linewidth=1,color='k',linestyle='--') plt.ylim([0,1.1]) plt.xlabel('p(i=1)') plt.ylabel('Impurity Index') plt.show()

決策分類結果：

決策分類GraphViz圖：

隨機森林結果：

信息增益：熵、基尼、誤分類率對純度的影響：

總結

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