CART決策樹
前言
CART算法的全稱是Classification And Regression Tree，採用的是Gini指數（選Gini指數最小的特徵s）做爲分裂標準，是一種實用的分類算法。node
1、CART決策樹算法
主要思路是對一個數據集選擇幾個屬性做爲特徵，對於每一個特徵提出一個劃分條件，根據這個條件將結點分爲兩個子節點，對於子節點一樣利用下一個特徵進行劃分，直到某結點的Gini值符合要求，咱們認爲這個結點的不純性很小，該節點已成功分類。如此反覆執行，最後能夠獲得由若干個結點組成的決策樹，其中的每一個葉節點都是分類的結果。python
某結點的Gini值的計算公式以下：
若是要對某種劃分計算Gini值，能夠利用加權平均，即：
算法
明確了Gini值的計算以及決策樹的基本思路後，就能夠繼續向下看具體的代碼實現了，本文沒有使用sklearn庫，若是讀者只是須要使用該算法，而不想了解算法實際的實現思路的話，能夠無需向下看了。
數組
2、Python代碼實現
主要分爲6個步驟：app
- 尋找到最佳屬性
- 建立決策樹
- 將上一結點分裂，分別計算左、右子節點的Gini值。
- 計算Gnin值有一種方法：將數據集對應這個屬性的值排序，從頭開始選擇相鄰兩個值的平均值做爲劃分條件，計算該分發下的Gini值，如此遍歷一遍，選出最小的一個Gini值對應的劃分條件，做爲該屬性的最佳分裂條件
- 對於子節點，Gini值小於閾值，認爲其是葉節點，結束這一方向的分裂。若Gini值大於閾值，認爲分類還不夠純，需繼續分裂，下一次分裂要使用不一樣的屬性值。
- 遞歸調用建立決策樹，就能夠獲得完整的決策樹。
使用到的函數主要有5個：機器學習
- calcGini(dataSet) #計算結點GINI值
- splitDataSet(dataSet, n, value, type) #根據條件分離數據集
- FindBestFeature(dataSet) #選擇最好的特徵劃分數據集，即返回最佳特徵下標及傳入數據集各列的Gini指數
- createTree(dataSet, features, decisionTree) #生成決策樹。輸入：訓練數據集D，特徵集A。輸出：決策樹T
- testTree(dataSet) #得到測試結果，給出混淆矩陣
1.計算結點GINI值
def calcGini(dataSet): numTotal = dataSet.shape[0] # 記錄本數據集總條數 length = len(dataSet[0]) # 計算特徵列數 frequent_0 = 0.0 # 記錄三種樣本出現次數 frequent_1 = 0.0 frequent_2 = 0.0 for i in range(0,numTotal): if dataSet[i][length-1] == '0.0': frequent_0 += 1 elif dataSet[i][length-1] == '1.0': frequent_1 += 1 elif dataSet[i][length-1] == '2.0': frequent_2 += 1 gini = 1 - (frequent_0/numTotal)**2 - (frequent_1/numTotal)**2 - (frequent_2/numTotal)**2 return gini
2.分離數據集
def splitDataSet(dataSet, n, value, type): subDataSet = [] numTotal = dataSet.shape[0] # 記錄本數據集總條數 if type == 1: # type==1對應小於等於value的狀況 for i in range(0,numTotal): if float(dataSet[i][n]) <= value: subDataSet.append(dataSet[i]) elif type == 2: # type==2對應大於value的狀況 for i in range(0,numTotal): if float(dataSet[i][n]) > value: subDataSet.append(dataSet[i]) subDataSet = np.array(subDataSet) # 強制轉換爲array類型 return subDataSet,len(subDataSet)
3.選擇最好的特徵
def FindBestFeature(dataSet): numTotal = dataSet.shape[0] # 記錄本數據集總條數 numFeatures = len(dataSet[0]) - 2 # 計算特徵列數 bestFeature = -1 # 初始化參數，記錄最優特徵列i，下標從0開始 columnFeaGini={ } # 初始化參數，記錄每一列x的每一種特徵的基尼 Gini(D,A) for i in range(1, numFeatures+1): # 遍歷全部x特徵列,i爲特徵標號 featList = list(dataSet[:, i]) # 取這一列x中全部數據，轉換爲list類型 featListSort = [float(x) for x in featList] featListSort.sort() # 對該特徵值排序 FeaGinis = [] FeaGiniv = [] for j in range(0,len(featListSort)-1): # j爲第幾組數據 value = (featListSort[j]+featListSort[j+1])/2 feaGini = 0.0 subDataSet1,sublen1 = splitDataSet(dataSet, i, value, 1) # 獲取切分後的數據 subDataSet2,sublen2 = splitDataSet(dataSet, i, value, 2) feaGini = (sublen1/numTotal) * calcGini(subDataSet1) + (sublen2/numTotal) * calcGini(subDataSet2) # 計算此分法對應Gini值 FeaGinis.append(feaGini) # 記錄該特徵下各類分法遍歷出的Gini值 FeaGiniv.append(value) # 記錄該特徵下的各類分法 columnFeaGini['%d_%f'%(i,FeaGiniv[FeaGinis.index(min(FeaGinis))])] = min(FeaGinis) # 將該特徵下最小的Gini值 bestFeature = min(columnFeaGini, key=columnFeaGini.get) # 找到最小的Gini指數對應的數據列 return bestFeature,columnFeaGini
4.生成決策樹
def createTree(dataSet, features, decisionTree): if len(features) > 2: #特徵未用完 bestFeature, columnFeaGini = FindBestFeature(dataSet) bestFeatureLable = features[int(bestFeature.split('_')[0])] # 最佳特徵 NodeName = bestFeatureLable + '\n' +'<=' + bestFeature.split('_')[1] #結點名稱 decisionTree = { NodeName: { }} # 構建樹，以Gini指數最小的特徵bestFeature爲子節點 else: return decisionTree LeftSet, LeftSet_len = splitDataSet(dataSet, int(bestFeature.split('_')[0]), float(bestFeature.split('_')[1]), 1) RightSet, RightSet_len = splitDataSet(dataSet, int(bestFeature.split('_')[0]), float(bestFeature.split('_')[1]), 2) del (features[int(bestFeature.split('_')[0])]) # 該特徵已爲子節點使用，則刪除，以便接下來繼續構建子樹 if calcGini(LeftSet) <= 0.1 or len(features) == 2: L_lables_grp = dict(Counter(LeftSet[:,-1])) L_leaf = max(L_lables_grp, key=L_lables_grp.get) # 得到劃分後出現機率最大的分類做爲結點的分類 decisionTree[NodeName]['Y'] = L_leaf # 設定左枝葉子值 elif calcGini(LeftSet) > 0.1: dataSetNew = np.delete(LeftSet, int(bestFeature.split('_')[0]), axis=1) # 刪除此最優劃分x列，使用剩餘的x列進行數據劃分 L_subFeatures = features[:] decisionTree[NodeName]['Y'] = { 'NONE'} decisionTree[NodeName]['Y'] = createTree(dataSetNew, L_subFeatures, decisionTree[NodeName]['Y']) #遞歸生成左邊的樹 if calcGini(RightSet) <= 0.1 or len(features) == 2: R_lables_grp = dict(Counter(RightSet[:,-1])) R_leaf = max(R_lables_grp, key=R_lables_grp.get) # 得到劃分後出現機率最大的分類做爲結點的分類 decisionTree[NodeName]['N'] = R_leaf # 設定右枝葉子值 elif calcGini(RightSet) > 0.1: dataSetNew = np.delete(RightSet, int(bestFeature.split('_')[0]), axis=1) # 刪除此最優劃分x列，使用剩餘的x列進行數據劃分 R_subFeatures = features[:] decisionTree[NodeName]['N'] = { 'NONE'} decisionTree[NodeName]['N'] = createTree(dataSetNew, R_subFeatures, decisionTree[NodeName]['N']) #遞歸生成右邊的樹 return decisionTree
5.測試決策樹
def testTree(dataSet): numTotal = dataSet.shape[0] # 記錄本數據集總條數 testmemory = [] label = dataSet[:,-1] TP = 0 FP = 0 TN = 0 FN = 0 for i in range(0,numTotal): if float(dataSet[i][4]) <= 0.001444: #標準差 if float(dataSet[i][1]) <= 0.01022: #均值 if float(dataSet[i][6]) <= -0.589019: #峯度 testmemory.append('0.0') else: if float(dataSet[i][3]) <= -0.001811: #四分位差 if float(dataSet[i][2]) <= -0.000026: #中位數 testmemory.append('0.0') else: testmemory.append('2.0') else: if float(dataSet[i][2]) <= 0.007687: #中位數 if float(dataSet[i][5]) <= 0.452516: #偏度 testmemory.append('0.0') else: testmemory.append('0.0') else: testmemory.append('2.0') else: testmemory.append('2.0') else: if float(dataSet[i][3]) <= -0.013691: # 四分位差 testmemory.append('1.0') else: if float(dataSet[i][5]) <= 1.462280: #偏度 if float(dataSet[i][6]) <= -1.034223: # 峯度 if float(dataSet[i][1]) <= 0.009173: # 均值 if float(dataSet[i][2]) <= -0.004193: # 中位數 testmemory.append('2.0') else: testmemory.append('2.0') else: testmemory.append('0.0') else: testmemory.append('2.0') else: if float(dataSet[i][1]) <= -0.023631: # 均值 testmemory.append('2.0') else: testmemory.append('1.0') for i in range(0, numTotal): if (testmemory[i] == '1.0') and (label[i] == '1.0'): TP += 1 elif (testmemory[i] == '1.0') and (label[i] != '1.0'): FP += 1 elif (testmemory[i] != '1.0') and (label[i] != '1.0'): TN += 1 elif (testmemory[i] != '1.0') and (label[i] == '1.0'): FN += 1 print('TP:%d' % TP) #真陽性 print('FP:%d' % FP) #假陽性 print('TN:%d' % TN) #真陰性 print('FN:%d' % FN) #假陰性 cm = confusion_matrix(label, testmemory, labels=["0.0", "1.0", "2.0"]) plt.rc('figure', figsize=(5, 5)) plt.matshow(cm, cmap=plt.cm.cool) # 背景顏色 plt.colorbar() # 顏色標籤 # 內部添加圖例標籤 for x in range(len(cm)): for y in range(len(cm)): plt.annotate(cm[x, y], xy=(y, x), horizontalalignment='center', verticalalignment='center') plt.ylabel('True Label') plt.xlabel('Predicted Label') plt.title('decision_tree') plt.savefig(r'confusion_matrix')
6.決策樹可視化
可視化部分基本摘自《機器學習實戰》第三章。函數
matplotlib.rcParams['font.family']='SimHei' # 用來正常顯示中文 plt.rcParams['axes.unicode_minus']=False # 用來正常顯示負號 decisionNode = dict(boxstyle="sawtooth", fc="0.8") leafNode = dict(boxstyle="round4", fc="0.8") arrow_args = dict(arrowstyle="<-") def getNumLeafs(myTree): numLeafs = 0 firstStr = list(myTree.keys())[0] secondDict = myTree[firstStr] for key in secondDict.keys(): if type(secondDict[ key]).__name__ == 'dict': # test to see if the nodes are dictonaires, if not they are leaf nodes numLeafs += getNumLeafs(secondDict[key]) else: numLeafs += 1 return numLeafs def getTreeDepth(myTree): maxDepth = 0 firstStr = list(myTree.keys())[0] # myTree.keys()[0] secondDict = myTree[firstStr] for key in secondDict.keys(): if type(secondDict[ key]).__name__ == 'dict': # test to see if the nodes are dictonaires, if not they are leaf nodes thisDepth = 1 + getTreeDepth(secondDict[key]) else: thisDepth = 1 if thisDepth > maxDepth: maxDepth = thisDepth return maxDepth def plotNode(nodeTxt, centerPt, parentPt, nodeType): createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction', xytext=centerPt, textcoords='axes fraction', va="center", ha="center", bbox=nodeType, arrowprops=arrow_args) def plotMidText(cntrPt, parentPt, txtString): xMid = (parentPt[0] - cntrPt[0]) / 2.0 + cntrPt[0] yMid = (parentPt[1] - cntrPt[1]) / 2.0 + cntrPt[1] createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30) def plotTree(myTree, parentPt, nodeTxt): # if the first key tells you what feat was split on numLeafs = getNumLeafs(myTree) # this determines the x width of this tree # depth = getTreeDepth(myTree) firstStr = list(myTree.keys())[0] # myTree.keys()[0] #the text label for this node should be this cntrPt = (plotTree.xOff + (1.0 + float(numLeafs)) / 2.0 / plotTree.totalW, plotTree.yOff) plotMidText(cntrPt, parentPt, nodeTxt) plotNode(firstStr, cntrPt, parentPt, decisionNode) secondDict = myTree[firstStr] plotTree.yOff = plotTree.yOff - 1.0 / plotTree.totalD for key in secondDict.keys(): if type(secondDict[ key]).__name__ == 'dict': # test to see if the nodes are dictonaires, if not they are leaf nodes plotTree(secondDict[key], cntrPt, str(key)) # recursion else: # it's a leaf node print the leaf node plotTree.xOff = plotTree.xOff + 1.0 / plotTree.totalW plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode) plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key)) plotTree.yOff = plotTree.yOff + 1.0 / plotTree.totalD def createPlot(myTree): fig = plt.figure(1, facecolor='white') fig.clf() axprops = dict(xticks=[], yticks=[]) createPlot.ax1 = plt.subplot(111, frameon=False, **axprops) # no ticks # createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses plotTree.totalW = float(getNumLeafs(myTree)) plotTree.totalD = float(getTreeDepth(myTree)) plotTree.xOff = -0.5 / plotTree.totalW; plotTree.yOff = 1.0; plotTree(myTree, (0.5, 1.0), '') plt.show()
7.主程序部分
trainingData, testingData= read_xslx(r'e:/Table/機器學習/1109/attribute_113.xlsx') features = list(trainingData[0]) # x的表頭,即特徵 trainingDataSet = trainingData[1:] # 訓練集 bestFeature, columnFeaGini=FindBestFeature(trainingDataSet) decisionTree = { } decisiontree = createTree(trainingDataSet, features, decisionTree) # 創建決策樹，CART分類樹 print('CART分類樹：\n', decisiontree) testTree(testingData) createPlot(decisiontree)
CART決策分類樹全部代碼
# -*- coding: utf-8 -*- 支持文件中出現中文字符 ######################################################################### """ Created on Mon Nov 16 21:26:00 2020 @author: ixobgenw 代碼功能描述： （1）計算結點GINI值 （2）分離數據集 （3）選擇最好的特徵 （4）生成決策樹 （5）測試決策樹 """ ##################################################################### import xlrd import numpy as np from collections import Counter import matplotlib.pyplot as plt import matplotlib #可視化部分 #################################################################################################################### matplotlib.rcParams['font.family']='SimHei' # 用來正常顯示中文 plt.rcParams['axes.unicode_minus']=False # 用來正常顯示負號 decisionNode = dict(boxstyle="sawtooth", fc="0.8") leafNode = dict(boxstyle="round4", fc="0.8") arrow_args = dict(arrowstyle="<-") def getNumLeafs(myTree): numLeafs = 0 firstStr = list(myTree.keys())[0] secondDict = myTree[firstStr] for key in secondDict.keys(): if type(secondDict[ key]).__name__ == 'dict': # test to see if the nodes are dictonaires, if not they are leaf nodes numLeafs += getNumLeafs(secondDict[key]) else: numLeafs += 1 return numLeafs def getTreeDepth(myTree): maxDepth = 0 firstStr = list(myTree.keys())[0] # myTree.keys()[0] secondDict = myTree[firstStr] for key in secondDict.keys(): if type(secondDict[ key]).__name__ == 'dict': # test to see if the nodes are dictonaires, if not they are leaf nodes thisDepth = 1 + getTreeDepth(secondDict[key]) else: thisDepth = 1 if thisDepth > maxDepth: maxDepth = thisDepth return maxDepth def plotNode(nodeTxt, centerPt, parentPt, nodeType): createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction', xytext=centerPt, textcoords='axes fraction', va="center", ha="center", bbox=nodeType, arrowprops=arrow_args) def plotMidText(cntrPt, parentPt, txtString): xMid = (parentPt[0] - cntrPt[0]) / 2.0 + cntrPt[0] yMid = (parentPt[1] - cntrPt[1]) / 2.0 + cntrPt[1] createPlot.ax1.text(xMid, yMid, txtString, va="center", ha="center", rotation=30) def plotTree(myTree, parentPt, nodeTxt): # if the first key tells you what feat was split on numLeafs = getNumLeafs(myTree) # this determines the x width of this tree # depth = getTreeDepth(myTree) firstStr = list(myTree.keys())[0] # myTree.keys()[0] #the text label for this node should be this cntrPt = (plotTree.xOff + (1.0 + float(numLeafs)) / 2.0 / plotTree.totalW, plotTree.yOff) plotMidText(cntrPt, parentPt, nodeTxt) plotNode(firstStr, cntrPt, parentPt, decisionNode) secondDict = myTree[firstStr] plotTree.yOff = plotTree.yOff - 1.0 / plotTree.totalD for key in secondDict.keys(): if type(secondDict[ key]).__name__ == 'dict': # test to see if the nodes are dictonaires, if not they are leaf nodes plotTree(secondDict[key], cntrPt, str(key)) # recursion else: # it's a leaf node print the leaf node plotTree.xOff = plotTree.xOff + 1.0 / plotTree.totalW plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode) plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key)) plotTree.yOff = plotTree.yOff + 1.0 / plotTree.totalD def createPlot(myTree): fig = plt.figure(1, facecolor='white') fig.clf() axprops = dict(xticks=[], yticks=[]) createPlot.ax1 = plt.subplot(111, frameon=False, **axprops) # no ticks # createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses plotTree.totalW = float(getNumLeafs(myTree)) plotTree.totalD = float(getTreeDepth(myTree)) plotTree.xOff = -0.5 / plotTree.totalW; plotTree.yOff = 1.0; plotTree(myTree, (0.5, 1.0), '') plt.show() #################################################################################################################### #讀取excel文件,70%爲訓練集，30%爲測試集 #################################################################################################################### def read_xslx(xslx_path): trainingdata = [] # 先聲明一個空list testingdata = [] data = xlrd.open_workbook(xslx_path) # 讀取文件 table = data.sheet_by_index(0) # 按索引獲取工做表，0就是工做表1 for i in range(int(0.7*table.nrows)): # table.nrows表示總行數 line = table.row_values(i) # 讀取每行數據，保存在line裏面，line是list trainingdata.append(line) # 將line加入到trainingdata中，trainingdata是二維list trainingdata = np.array(trainingdata) # 將trainingdata從二維list變成數組 for i in range(int(0.7*table.nrows),int(table.nrows)): # table.nrows表示總行數 line = table.row_values(i) # 讀取每行數據，保存在line裏面，line是list testingdata.append(line) # 將line加入到testingdata中，testingdata是二維list testingdata = np.array(testingdata) # 將testingdata從二維list變成數組 return trainingdata,testingdata #################################################################################################################### #計算結點GINI值 #################################################################################################################### def calcGini(dataSet): numTotal = dataSet.shape[0] # 記錄本數據集總條數 length = len(dataSet[0]) # 計算特徵列數 frequent_0 = 0.0 # 記錄三種樣本出現次數 frequent_1 = 0.0 frequent_2 = 0.0 for i in range(0,numTotal): if dataSet[i][length-1] == '0.0': frequent_0 += 1 elif dataSet[i][length-1] == '1.0': frequent_1 += 1 elif dataSet[i][length-1] == '2.0': frequent_2 += 1 gini = 1 - (frequent_0/numTotal)**2 - (frequent_1/numTotal)**2 - (frequent_2/numTotal)**2 return gini #################################################################################################################### #根據條件分離數據集 #################################################################################################################### def splitDataSet(dataSet, n, value, type): subDataSet = [] numTotal = dataSet.shape[0] # 記錄本數據集總條數 if type == 1: # type==1對應小於等於value的狀況 for i in range(0,numTotal): if float(dataSet[i][n]) <= value: subDataSet.append(dataSet[i]) elif type == 2: # type==2對應大於value的狀況 for i in range(0,numTotal): if float(dataSet[i][n]) > value: subDataSet.append(dataSet[i]) subDataSet = np.array(subDataSet) # 強制轉換爲array類型 return subDataSet,len(subDataSet) #################################################################################################################### #選擇最好的特徵劃分數據集，即返回最佳特徵下標及傳入數據集各列的Gini指數 #################################################################################################################### def FindBestFeature(dataSet): numTotal = dataSet.shape[0] # 記錄本數據集總條數 numFeatures = len(dataSet[0]) - 2 # 計算特徵列數 bestFeature = -1 # 初始化參數，記錄最優特徵列i，下標從0開始 columnFeaGini={ } # 初始化參數，記錄每一列x的每一種特徵的基尼 Gini(D,A) for i in range(1, numFeatures+1): # 遍歷全部x特徵列,i爲特徵標號 featList = list(dataSet[:, i]) # 取這一列x中全部數據，轉換爲list類型 featListSort = [float(x) for x in featList] featListSort.sort() # 對該特徵值排序 FeaGinis = [] FeaGiniv = [] for j in range(0,len(featListSort)-1): # j爲第幾組數據 value = (featListSort[j]+featListSort[j+1])/2 feaGini = 0.0 subDataSet1,sublen1 = splitDataSet(dataSet, i, value, 1) # 獲取切分後的數據 subDataSet2,sublen2 = splitDataSet(dataSet, i, value, 2) feaGini = (sublen1/numTotal) * calcGini(subDataSet1) + (sublen2/numTotal) * calcGini(subDataSet2) # 計算此分法對應Gini值 FeaGinis.append(feaGini) # 記錄該特徵下各類分法遍歷出的Gini值 FeaGiniv.append(value) # 記錄該特徵下的各類分法 columnFeaGini['%d_%f'%(i,FeaGiniv[FeaGinis.index(min(FeaGinis))])] = min(FeaGinis) # 將該特徵下最小的Gini值 bestFeature = min(columnFeaGini, key=columnFeaGini.get) # 找到最小的Gini指數對應的數據列 return bestFeature,columnFeaGini #################################################################################################################### #生成決策樹。輸入：訓練數據集D，特徵集A。輸出：決策樹T #################################################################################################################### def createTree(dataSet, features, decisionTree): if len(features) > 2: #特徵未用完 bestFeature, columnFeaGini = FindBestFeature(dataSet) bestFeatureLable = features[int(bestFeature.split('_')[0])] # 最佳特徵 NodeName = bestFeatureLable + '\n' +'<=' + bestFeature.split('_')[1] #結點名稱 decisionTree = { NodeName: { }} # 構建樹，以Gini指數最小的特徵bestFeature爲子節點 else: return decisionTree LeftSet, LeftSet_len = splitDataSet(dataSet, int(bestFeature.split('_')[0]), float(bestFeature.split('_')[1]), 1) RightSet, RightSet_len = splitDataSet(dataSet, int(bestFeature.split('_')[0]), float(bestFeature.split('_')[1]), 2) del (features[int(bestFeature.split('_')[0])]) # 該特徵已爲子節點使用，則刪除，以便接下來繼續構建子樹 if calcGini(LeftSet) <= 0.1 or len(features) == 2: L_lables_grp = dict(Counter(LeftSet[:,-1])) L_leaf = max(L_lables_grp, key=L_lables_grp.get) # 得到劃分後出現機率最大的分類做爲結點的分類 decisionTree[NodeName]['Y'] = L_leaf # 設定左枝葉子值 elif calcGini(LeftSet) > 0.1: dataSetNew = np.delete(LeftSet, int(bestFeature.split('_')[0]), axis=1) # 刪除此最優劃分x列，使用剩餘的x列進行數據劃分 L_subFeatures = features[:] decisionTree[NodeName]['Y'] = { 'NONE'} decisionTree[NodeName]['Y'] = createTree(dataSetNew, L_subFeatures, decisionTree[NodeName]['Y']) #遞歸生成左邊的樹 if calcGini(RightSet) <= 0.1 or len(features) == 2: R_lables_grp = dict(Counter(RightSet[:,-1])) R_leaf = max(R_lables_grp, key=R_lables_grp.get) # 得到劃分後出現機率最大的分類做爲結點的分類 decisionTree[NodeName]['N'] = R_leaf # 設定右枝葉子值 elif calcGini(RightSet) > 0.1: dataSetNew = np.delete(RightSet, int(bestFeature.split('_')[0]), axis=1) # 刪除此最優劃分x列，使用剩餘的x列進行數據劃分 R_subFeatures = features[:] decisionTree[NodeName]['N'] = { 'NONE'} decisionTree[NodeName]['N'] = createTree(dataSetNew, R_subFeatures, decisionTree[NodeName]['N']) #遞歸生成右邊的樹 return decisionTree #################################################################################################################### #得到測試結果 #################################################################################################################### def testTree(dataSet): numTotal = dataSet.shape[0] # 記錄本數據集總條數 testmemory = [] label = dataSet[:,-1] TP = 0 FP = 0 TN = 0 FN = 0 for i in range(0,numTotal): if float(dataSet[i][4]) <= 0.001444: #標準差 if float(dataSet[i][1]) <= 0.01022: #均值 if float(dataSet[i][6]) <= -0.589019: #峯度 testmemory.append('0.0') else: if float(dataSet[i][3]) <= -0.001811: #四分位差 if float(dataSet[i][2]) <= -0.000026: #中位數 testmemory.append('0.0') else: testmemory.append('2.0') else: if float(dataSet[i][2]) <= 0.007687: #中位數 if float(dataSet[i][5]) <= 0.452516: #偏度 testmemory.append('0.0') else: testmemory.append('0.0') else: testmemory.append('2.0') else: testmemory.append('2.0') else: if float(dataSet[i][3]) <= -0.013691: # 四分位差 testmemory.append('1.0') else: if float(dataSet[i][5]) <= 1.462280: #偏度 if float(dataSet[i][6]) <= -1.034223: # 峯度 if float(dataSet[i][1]) <= 0.009173: # 均值 if float(dataSet[i][2]) <= -0.004193: # 中位數 testmemory.append('2.0') else: testmemory.append('2.0') else: testmemory.append('0.0') else: testmemory.append('2.0') else: if float(dataSet[i][1]) <= -0.023631: # 均值 testmemory.append('2.0') else: testmemory.append('1.0') for i in range(0, numTotal): if (testmemory[i] == '1.0') and (label[i] == '1.0'): TP += 1 elif (testmemory[i] == '1.0') and (label[i] != '1.0'): FP += 1 elif (testmemory[i] != '1.0') and (label[i] != '1.0'): TN += 1 elif (testmemory[i] != '1.0') and (label[i] == '1.0'): FN += 1 print('TP:%d' % TP) #真陽性 print('FP:%d' % FP) #假陽性 print('TN:%d' % TN) #真陰性 print('FN:%d' % FN) #假陰性 cm = confusion_matrix(label, testmemory, labels=["0.0", "1.0", "2.0"]) plt.rc('figure', figsize=(5, 5)) plt.matshow(cm, cmap=plt.cm.cool) # 背景顏色 plt.colorbar() # 顏色標籤 # 內部添加圖例標籤 for x in range(len(cm)): for y in range(len(cm)): plt.annotate(cm[x, y], xy=(y, x), horizontalalignment='center', verticalalignment='center') plt.ylabel('True Label') plt.xlabel('Predicted Label') plt.title('decision_tree') plt.savefig(r'confusion_matrix') #################################################################################################################### trainingData, testingData= read_xslx(r'e:/Table/機器學習/1109/attribute_113.xlsx') features = list(trainingData[0]) # x的表頭,即特徵 trainingDataSet = trainingData[1:] # 訓練集 bestFeature, columnFeaGini=FindBestFeature(trainingDataSet) decisionTree = { } decisiontree = createTree(trainingDataSet, features, decisionTree) # 創建決策樹，CART分類樹 print('CART分類樹：\n', decisiontree) testTree(testingData) createPlot(decisiontree)
3、運行結果
CART分類樹：
{‘標準差\n<=0.001444’: {‘Y’: {‘均值\n<=0.010220’: {‘Y’: {‘峯度\n<=-0.589019’: {‘Y’: ‘0.0’, ‘N’: {‘四分位差\n<=-0.001811’: {‘Y’: {‘中位數\n<=-0.000026’: {‘Y’: ‘0.0’, ‘N’: ‘2.0’}}, ‘N’: {‘中位數\n<=0.007687’: {‘Y’: {‘偏度\n<=0.452516’: {‘Y’: ‘0.0’, ‘N’: ‘0.0’}}, ‘N’: ‘2.0’}}}}}}, ‘N’: ‘2.0’}}, ‘N’: {‘四分位差\n<=-0.013691’: {‘Y’: ‘1.0’, ‘N’: {‘偏度\n<=1.462280’: {‘Y’: {‘峯度\n<=-1.034223’: {‘Y’: {‘均值\n<=0.009173’: {‘Y’: {‘中位數\n<=-0.004193’: {‘Y’: ‘2.0’, ‘N’: ‘2.0’}}, ‘N’: ‘0.0’}}, ‘N’: ‘2.0’}}, ‘N’: {‘均值\n<=-0.023631’: {‘Y’: ‘2.0’, ‘N’: ‘1.0’}}}}}}}}
學習
混淆矩陣：
若是將「1」看作一類，「0」和「2」看作一類，結果爲：
TP:13
FP:0
TN:74
FN:3
測試
若是每種標籤都看作一類，則混淆矩陣爲：
this