有點亂，等我徹底想明白時再來整理清楚。
from math import log import operator def calcShannonEnt(dataSet): numEntries = len(dataSet) #print("樣本總數：" + str(numEntries)) labelCounts = {} #記錄每一類標籤的數量 #定義特徵向量featVec for featVec in dataSet: currentLabel = featVec[-1] #最後一列是類別標籤 if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0; labelCounts[currentLabel] += 1 #標籤currentLabel出現的次數 #print("當前labelCounts狀態：" + str(labelCounts)) shannonEnt = 0.0 for key in labelCounts: prob = float(labelCounts[key]) / numEntries #每一個類別標籤出現的概率 #print(str(key) + "類別的概率：" + str(prob)) #print(prob * log(prob, 2) ) shannonEnt -= prob * log(prob, 2) #print("熵值：" + str(shannonEnt)) return shannonEnt def createDataSet(): dataSet = [ [1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no'], #以下隨意新增，用於測試熵的變化，越混亂越衝突，熵越大 # [1, 1, 'no'], # [1, 1, 'no'], # [1, 1, 'no'], # [1, 1, 'no'], #[1, 1, 'maybe'], # [1, 1, 'maybe1'] # 用下面的8個比較極端的例子看得會更清楚。如果按照這個規則繼續增加下去，熵會繼續增大。 # [1,1,'1'], # [1,1,'2'], # [1,1,'3'], # [1,1,'4'], # [1,1,'5'], # [1,1,'6'], # [1,1,'7'], # [1,1,'8'], # 這是另一個極端的例子，所有樣本的類別是一樣的，有序，不混亂，此時熵為0 # [1,1,'2'], # [1,1,'1'], # [1,1,'1'], # [1,1,'1'], # [1,1,'1'], # [1,1,'1'], # [1,1,'1'], # [1,1,'1'], ] #print("dataSet[0]：" + str(dataSet[0])) #print(dataSet) labels = ['no surfacing', 'flippers'] return dataSet, labels def testCalcShannonEnt(): myDat, labels = createDataSet() #print(calcShannonEnt(myDat)) def splitDataSet(dataSet, axis, value): retDataSet = [] for featVec in dataSet: #print("featVec：" + str(featVec)) #print("featVec[axis]：" + str(featVec[axis])) if featVec[axis] == value: reduceFeatVec = featVec[:axis] #print(reduceFeatVec) reduceFeatVec.extend(featVec[axis + 1:]) #print('reduceFeatVec：' + str(reduceFeatVec)) retDataSet.append(reduceFeatVec) #print("retDataSet：" + str(retDataSet)) return retDataSet def testSplitDataSet(): myDat,labels = createDataSet() #print(myDat) a = splitDataSet(myDat, 0, 0) #print(a) def chooseBestFeatureToSplit(dataSet): numFeatures = len(dataSet[0]) - 1 #減掉類別列，剩2列 #print("特徵數量：" + str(numFeatures)) baseEntropy = calcShannonEnt(dataSet) #print("基礎熵：" + str(baseEntropy)) bestInfoGain = 0.0; bestFeature = -1 #numFeatures==2 for i in range(numFeatures): #print("i的值" + str(i)) featList = [example[i] for example in dataSet]; #print("featList：" + str(featList)) #在列表中建立集合是Python語言得到列表中唯一元素值的最快方法 #集合物件是一組無序排列的可雜湊的值。集合化，收縮 #[1, 0, 1, 1, 1, 1]建立集合後，變為{0,1} uniqueVals = set(featList) #print("uniqueVals" + str(uniqueVals)) newEntropy = 0.0 #uniqueVals=={0,1} for value in uniqueVals: subDataSet = splitDataSet(dataSet, i, value) #print("subDataSet:" + str(subDataSet)) prob = len(subDataSet) / float(len(dataSet)) #print("subDataSet:" + str(subDataSet)) #print("subDataSet的長度：" + str(len(subDataSet))) newEntropy += prob * calcShannonEnt(subDataSet) #print("newEntropy：" + str(newEntropy)) #資訊增益，新序列熵越小，增益越大，最終目標是把最大的增益找出來 infoGain = baseEntropy - newEntropy #print("infoGain:" + str(infoGain)) #print("bestInfoGain:" + str(bestInfoGain)) if(infoGain > bestInfoGain): bestInfoGain = infoGain bestFeature = i #print("bestFeature：" + str(bestFeature)) return bestFeature def testChooseBestFeatureToSplit(): myDat, labels = createDataSet() chooseBestFeatureToSplit(myDat) ''' 輸入：類別列表 輸出：類別列表中多數的類，即多數表決 這個函式的作用是返回字典中出現次數最多的value對應的key，也就是輸入list中出現最多的那個值 ''' def majorityCnt(classList): classCount={} for vote in classList: if vote not in classCount.keys(): classCount[vote] = 0 classCount[vote] += 1 #key=operator.itemgetter(0)或key=operator.itemgetter(1)，決定以字典的鍵排序還是以字典的值排序 #0以鍵排序，1以值排序 #reverse（是否反轉）預設是False，reverse == true 則反轉由大到小排列 sortedClassCount = sorted(classCount.items(), key=operator.itemgetter(1), reverse=True) print(sortedClassCount) return sortedClassCount[0][0] def testMajorityCnt(): list1 = ['a','b','a','a','b','c','d','d','d','e','a','a','a','a','c','c','c','c','c','c','c','c'] print(majorityCnt(list1)) global n n=0 def createTree(dataSet, labels): global n print("=================createTree"+str(n)+" begin=============") n += 1 print(n) classList = [example[-1] for example in dataSet] print("第" + str(n) + "次classList:" + str(classList)) print("此時列表中的第1個元素為" + str(classList[0]) + "，數量為：" + str(classList.count(classList[0])) + "，列表總長度為：" + str(len(classList))) print("列表中"+str(classList[0])+"的數量：",classList.count(classList[0])) print("列表的長度：", len(classList)) if classList.count(classList[0])== len(classList): print("判斷結果為：所有類別相同，停止本組劃分") else: print("判斷結果為：類別不相同") #列表中有n個元素，並且n個都一致，則停止遞迴 if classList.count(classList[0]) == len(classList): return classList[0] print("dataSet[0]:" + str(dataSet[0])) if len(dataSet[0]) == 1: print("啟動多數表決") #書中的示例樣本集合沒有觸發 return majorityCnt(classList) bestFeat = chooseBestFeatureToSplit(dataSet) bestFeatLabel = labels[bestFeat] print("bestFeat:" +str(bestFeat)) print("bestFeatLabel:" + str(bestFeatLabel)) myTree = {bestFeatLabel:{}} print("當前樹狀態：" + str(myTree)) print("當前標籤集合：" + str(labels)) print("準備刪除" + labels[bestFeat]) del(labels[bestFeat]) print("已刪除") print("刪除元素後的標籤集合：" + str(labels)) featValues = [example[bestFeat] for example in dataSet] print("featValues：",featValues) uniqueVals = set(featValues) print("uniqueVals：", uniqueVals) #{0,1} k = 0 print("********開始迴圈******") for value in uniqueVals: k += 1 print("第",k,"次迴圈") subLabels = labels[:] print("傳入引數：") print(" --待劃分的資料集：",dataSet) print(" --劃分資料集的特徵：", bestFeat) print(" --需要返回的符合特徵值：", value) splited = splitDataSet(dataSet, bestFeat, value) print("splited：", str(splited)) myTree[bestFeatLabel][value] = createTree(splited, subLabels) #遞迴呼叫 print("*******結束迴圈*****") print("=================createTree"+str(n)+" end=============") return myTree def testCreateTree(): myDat,labels = createDataSet(); myTree = createTree(myDat, labels); print("============testCreateTree=============") print(myTree) if __name__ == '__main__': #測試輸出資訊熵 #testCalcShannonEnt() #測試拆分結果集 #testSplitDataSet() #選擇最好的特徵值 #testChooseBestFeatureToSplit() #testMajorityCnt() testCreateTree()