目录
一、为什么要剪枝
二、剪枝的策略
1、预剪枝(pre-pruning)
2、后剪枝(post-pruning)
三、代码实现
1、收集、准备数据:
2、分析数据:
3、预剪枝及测试:
4、后剪枝及测试:
四、总结
一、为什么要剪枝
剪枝(pruning)的目的是为了避免决策树模型的过拟合。因为决策树算法在学习的过程中为了尽可能的正确的分类训练样本,不停地对结点进行划分,因此这会导致整棵树的分支过多,也就导致了过拟合。
二、剪枝的策略
决策树的剪枝策略最基本的有两种:预剪枝(pre-pruning)和后剪枝(post-pruning)
1、预剪枝(pre-pruning)
预剪枝:
文章来源:https://www.toymoban.com/news/detail-460949.html
2、后剪枝(post-pruning)
后剪枝就是先把整颗决策树构造完毕,然后自底向上的对非叶结点进行考察,若将该结点对应的子树换为叶结点能够带来泛华性能的提升,则把该子树替换为叶结点。
后剪枝处理:
三、代码实现
1、收集、准备数据:
这里采用上面西瓜2.0的数据集:
import math
import numpy as np
def createMyData():
data = np.array([['青绿', '蜷缩', '浊响', '清晰', '凹陷', '硬滑']
, ['乌黑', '蜷缩', '沉闷', '清晰', '凹陷', '硬滑']
, ['乌黑', '蜷缩', '浊响', '清晰', '凹陷', '硬滑']
, ['青绿', '蜷缩', '沉闷', '清晰', '凹陷', '硬滑']
, ['浅白', '蜷缩', '浊响', '清晰', '凹陷', '硬滑']
, ['青绿', '稍蜷', '浊响', '清晰', '稍凹', '软粘']
, ['乌黑', '稍蜷', '浊响', '稍糊', '稍凹', '软粘']
, ['乌黑', '稍蜷', '浊响', '清晰', '稍凹', '硬滑']
, ['乌黑', '稍蜷', '沉闷', '稍糊', '稍凹', '硬滑']
, ['青绿', '硬挺', '清脆', '清晰', '平坦', '软粘']
, ['浅白', '硬挺', '清脆', '模糊', '平坦', '硬滑']
, ['浅白', '蜷缩', '浊响', '模糊', '平坦', '软粘']
, ['青绿', '稍蜷', '浊响', '稍糊', '凹陷', '硬滑']
, ['浅白', '稍蜷', '沉闷', '稍糊', '凹陷', '硬滑']
, ['乌黑', '稍蜷', '浊响', '清晰', '稍凹', '软粘']
, ['浅白', '蜷缩', '浊响', '模糊', '平坦', '硬滑']
, ['青绿', '蜷缩', '沉闷', '稍糊', '稍凹', '硬滑']])
label = np.array(['是', '是', '是', '是', '是', '是', '是', '是', '否', '否', '否', '否', '否', '否', '否', '否', '否'])
name = np.array(['色泽', '根蒂', '敲声', '纹理', '脐部', '触感'])
return data, label, name
def splitMyData20(myData, myLabel):
myDataTrain = myData[[0, 1, 2, 5, 6, 9, 13, 14, 15, 16],:]
myDataTest = myData[[3, 4, 7, 8, 10, 11, 12],:]
myLabelTrain = myLabel[[0, 1, 2, 5, 6, 9, 13, 14, 15, 16]]
myLabelTest = myLabel[[3, 4, 7, 8, 10, 11, 12]]
return myDataTrain, myLabelTrain, myDataTest, myLabelTest
2、分析数据:
equalNums = lambda x,y: 0 if x is None else x[x==y].size
# 定义计算信息熵的函数
def singleEntropy(x):
x = np.asarray(x)
xValues = set(x)
entropy = 0
for xValue in xValues:
p = equalNums(x, xValue) / x.size
entropy -= p * math.log(p, 2)
return entropy
# 定义计算条件信息熵的函数
def conditionnalEntropy(feature, y):
feature = np.asarray(feature)
y = np.asarray(y)
featureValues = set(feature)
entropy = 0
for feat in featureValues:
p = equalNums(feature, feat) / feature.size
entropy += p * singleEntropy(y[feature == feat])
return entropy
# 定义信息增益
def infoGain(feature, y):
return singleEntropy(y) - conditionnalEntropy(feature, y)
# 定义信息增益率
def infoGainRatio(feature, y):
return 0 if singleEntropy(feature) == 0 else infoGain(feature, y) / singleEntropy(feature)
# 特征选取
def bestFeature(data, labels, method = 'id3'):
assert method in ['id3', 'c45'], "method 须为id3或c45"
data = np.asarray(data)
labels = np.asarray(labels)
# 根据输入的method选取 评估特征的方法:id3 -> 信息增益; c45 -> 信息增益率
def calcEnt(feature, labels):
if method == 'id3':
return infoGain(feature, labels)
elif method == 'c45' :
return infoGainRatio(feature, labels)
featureNum = data.shape[1]
bestEnt = 0
bestFeat = -1
for feature in range(featureNum):
ent = calcEnt(data[:, feature], labels)
if ent >= bestEnt:
bestEnt = ent
bestFeat = feature
return bestFeat, bestEnt
# 根据特征及特征值分割原数据集
def splitFeatureData(data, labels, feature):
features = np.asarray(data)[:,feature]
data = np.delete(np.asarray(data), feature, axis = 1)
labels = np.asarray(labels)
uniqFeatures = set(features)
dataSet = {}
labelSet = {}
for feat in uniqFeatures:
dataSet[feat] = data[features == feat]
labelSet[feat] = labels[features == feat]
return dataSet, labelSet
# 多数投票
def voteLabel(labels):
uniqLabels = list(set(labels))
labels = np.asarray(labels)
finalLabel = 0
labelNum = []
for label in uniqLabels:
labelNum.append(equalNums(labels, label))
return uniqLabels[labelNum.index(max(labelNum))]
# 创建决策树
def createTree(data, labels, names, method = 'id3'):
data = np.asarray(data)
labels = np.asarray(labels)
names = np.asarray(names)
if len(set(labels)) == 1:
return labels[0]
elif data.size == 0:
return voteLabel(labels)
bestFeat, bestEnt = bestFeature(data, labels, method = method)
bestFeatName = names[bestFeat]
names = np.delete(names, [bestFeat])
decisionTree = {bestFeatName: {}}
dataSet, labelSet = splitFeatureData(data, labels, bestFeat)
for featValue in dataSet.keys():
decisionTree[bestFeatName][featValue] = createTree(dataSet.get(featValue), labelSet.get(featValue), names, method)
return decisionTree
# 统计叶子节点数和树深度
def getTreeSize(decisionTree):
nodeName = list(decisionTree.keys())[0]
nodeValue = decisionTree[nodeName]
leafNum = 0
treeDepth = 0
leafDepth = 0
for val in nodeValue.keys():
if type(nodeValue[val]) == dict:
leafNum += getTreeSize(nodeValue[val])[0]
leafDepth = 1 + getTreeSize(nodeValue[val])[1]
else :
leafNum += 1
leafDepth = 1
treeDepth = max(treeDepth, leafDepth)
return leafNum, treeDepth
# 使用模型对其他数据分类
def dtClassify(decisionTree, rowData, names):
names = list(names)
feature = list(decisionTree.keys())[0]
featDict = decisionTree[feature]
feat = names.index(feature)
featVal = rowData[feat]
if featVal in featDict.keys():
if type(featDict[featVal]) == dict:
classLabel = dtClassify(featDict[featVal], rowData, names)
else:
classLabel = featDict[featVal]
return classLabel
使用Matplotlib注解绘制树形图:
import matplotlib.pyplot as plt
#定义文本框和箭头格式
decisionNode=dict(boxstyle="sawtooth",fc='0.8')
leafNode=dict(boxstyle="round4",fc='0.8')
arrow_args=dict(arrowstyle="<-")
#绘制带箭头的注释
def plotNode(nodeTxt,centerPt,parentPt,nodeType):
createPlot.axl.annotate(nodeTxt,xy=parentPt,xycoords='axes fraction',
xytext=centerPt,
textcoords='axes fraction',
va="center",ha="center",bbox=nodeType,arrowprops=arrow_args)
#获取叶节点的数目和树的层数
def getNumLeafs(myTree):
numLeafs=0
# firstStr=myTree.keys()[0]
firstStr=list(myTree.keys())[0]
secondDict=myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]).__name__=='dict':
numLeafs+=getNumLeafs(secondDict[key])
else:
numLeafs+=1
return numLeafs
def getTreeDepth(myTree):
maxDepth=0
firstStr=list(myTree.keys())[0]
secondDict=myTree[firstStr]
for key in secondDict.keys():
if type(secondDict[key]).__name__=='dict':
thisDepth=1+getTreeDepth(secondDict[key])
else:
thisDepth=1
if thisDepth>maxDepth:maxDepth=thisDepth
return maxDepth
def plotMidText(cntrPt,parentPt,txtString):
xMid=(parentPt[0]-cntrPt[0])/2.0+cntrPt[0]
yMid=(parentPt[1]-cntrPt[1])/2.0+cntrPt[1]
createPlot.axl.text(xMid,yMid,txtString)
def plotTree(mytree,parentPt,nodeTxt):
numLeafs=getNumLeafs(mytree)
depth=getTreeDepth(mytree)
firstStr=list(mytree.keys())[0]
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':
plotTree(secondDict[key],cntrPt,str(key))
else:
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(inTree):
fig=plt.figure(1,facecolor='white')
fig.clf()
axprops=dict(xticks=[],yticks=[])
createPlot.axl=plt.subplot(111,frameon=False,**axprops)
plotTree.totalW=float(getNumLeafs(inTree))
plotTree.totalD=float(getTreeDepth(inTree))
plotTree.xOff=-0.5/plotTree.totalW;plotTree.yOff=1.0;plotTree(inTree,(0.5,1.0),'')
plt.show()
3、预剪枝及测试:
# 创建预剪枝决策树
def createTreePrePruning(dataTrain, labelTrain, dataTest, labelTest, names, method = 'id3'):
trainData = np.asarray(dataTrain)
labelTrain = np.asarray(labelTrain)
testData = np.asarray(dataTest)
labelTest = np.asarray(labelTest)
names = np.asarray(names)
if len(set(labelTrain)) == 1:
return labelTrain[0]
elif trainData.size == 0:
return voteLabel(labelTrain)
bestFeat, bestEnt = bestFeature(dataTrain, labelTrain, method = method)
bestFeatName = names[bestFeat]
names = np.delete(names, [bestFeat])
dataTrainSet, labelTrainSet = splitFeatureData(dataTrain, labelTrain, bestFeat)
labelTrainLabelPre = voteLabel(labelTrain)
labelTrainRatioPre = equalNums(labelTrain, labelTrainLabelPre) / labelTrain.size
if dataTest is not None:
dataTestSet, labelTestSet = splitFeatureData(dataTest, labelTest, bestFeat)
labelTestRatioPre = equalNums(labelTest, labelTrainLabelPre) / labelTest.size
labelTrainEqNumPost = 0
for val in labelTrainSet.keys():
labelTrainEqNumPost += equalNums(labelTestSet.get(val), voteLabel(labelTrainSet.get(val))) + 0.0
labelTestRatioPost = labelTrainEqNumPost / labelTest.size
if dataTest is None and labelTrainRatioPre == 0.5:
decisionTree = {bestFeatName: {}}
for featValue in dataTrainSet.keys():
decisionTree[bestFeatName][featValue] = createTreePrePruning(dataTrainSet.get(featValue), labelTrainSet.get(featValue)
, None, None, names, method)
elif dataTest is None:
return labelTrainLabelPre
elif labelTestRatioPost < labelTestRatioPre:
return labelTrainLabelPre
else :
decisionTree = {bestFeatName: {}}
for featValue in dataTrainSet.keys():
decisionTree[bestFeatName][featValue] = createTreePrePruning(dataTrainSet.get(featValue), labelTrainSet.get(featValue)
, dataTestSet.get(featValue), labelTestSet.get(featValue)
, names, method)
return decisionTree
myDataTrain, myLabelTrain, myDataTest, myLabelTest = splitMyData20(myData, myLabel)
myTreeTrain = createTree(myDataTrain, myLabelTrain, myName, method = 'id3')
myTreePrePruning = createTreePrePruning(myDataTrain, myLabelTrain, myDataTest, myLabelTest, myName, method = 'id3')
# 画剪枝前的树
print("剪枝前的树")
createPlot(myTreeTrain)
# 画剪枝后的树
print("剪枝后的树")
createPlot(myTreePrePruning)
输出结果:
4、后剪枝及测试:
# 创建决策树 带预划分标签
def createTreeWithLabel(data, labels, names, method = 'id3'):
data = np.asarray(data)
labels = np.asarray(labels)
names = np.asarray(names)
votedLabel = voteLabel(labels)
if len(set(labels)) == 1:
return votedLabel
elif data.size == 0:
return votedLabel
bestFeat, bestEnt = bestFeature(data, labels, method = method)
bestFeatName = names[bestFeat]
names = np.delete(names, [bestFeat])
decisionTree = {bestFeatName: {"_vpdl": votedLabel}}
dataSet, labelSet = splitFeatureData(data, labels, bestFeat)
for featValue in dataSet.keys():
decisionTree[bestFeatName][featValue] = createTreeWithLabel(dataSet.get(featValue), labelSet.get(featValue), names, method)
return decisionTree
def convertTree(labeledTree):
labeledTreeNew = labeledTree.copy()
nodeName = list(labeledTree.keys())[0]
labeledTreeNew[nodeName] = labeledTree[nodeName].copy()
for val in list(labeledTree[nodeName].keys()):
if val == "_vpdl":
labeledTreeNew[nodeName].pop(val)
elif type(labeledTree[nodeName][val]) == dict:
labeledTreeNew[nodeName][val] = convertTree(labeledTree[nodeName][val])
return labeledTreeNew
# 后剪枝 训练完成后决策节点进行替换评估
def treePostPruning(labeledTree, dataTest, labelTest, names):
newTree = labeledTree.copy()
dataTest = np.asarray(dataTest)
labelTest = np.asarray(labelTest)
names = np.asarray(names)
featName = list(labeledTree.keys())[0]
featCol = np.argwhere(names==featName)[0][0]
names = np.delete(names, [featCol])
newTree[featName] = labeledTree[featName].copy()
featValueDict = newTree[featName]
featPreLabel = featValueDict.pop("_vpdl")
subTreeFlag = 0
dataFlag = 1 if sum(dataTest.shape) > 0 else 0
if dataFlag == 1:
dataTestSet, labelTestSet = splitFeatureData(dataTest, labelTest, featCol)
for featValue in featValueDict.keys():
if dataFlag == 1 and type(featValueDict[featValue]) == dict:
subTreeFlag = 1
newTree[featName][featValue] = treePostPruning(featValueDict[featValue], dataTestSet.get(featValue), labelTestSet.get(featValue), names)
if type(featValueDict[featValue]) != dict:
subTreeFlag = 0
if dataFlag == 0 and type(featValueDict[featValue]) == dict:
subTreeFlag = 1
newTree[featName][featValue] = convertTree(featValueDict[featValue])
if subTreeFlag == 0:
ratioPreDivision = equalNums(labelTest, featPreLabel) / labelTest.size
equalNum = 0
for val in labelTestSet.keys():
equalNum += equalNums(labelTestSet[val], featValueDict[val])
ratioAfterDivision = equalNum / labelTest.size
if ratioAfterDivision < ratioPreDivision:
newTree = featPreLabel
return newTree
myTreeTrain1 = createTreeWithLabel(myDataTrain, myLabelTrain, myName, method = 'id3')
createPlot(myTreeTrain1)
print(myTreeTrain1)
xgTreeBeforePostPruning = {"脐部": {"_vpdl": "是"
, '凹陷': {'色泽':{"_vpdl": "是", '青绿': '是', '乌黑': '是', '浅白': '否'}}
, '稍凹': {'根蒂':{"_vpdl": "是"
, '稍蜷': {'色泽': {"_vpdl": "是"
, '青绿': '是'
, '乌黑': {'纹理': {"_vpdl": "是"
, '稍糊': '是', '清晰': '否', '模糊': '是'}}
, '浅白': '是'}}
, '蜷缩': '否'
, '硬挺': '是'}}
, '平坦': '否'}}
xgTreePostPruning = treePostPruning(xgTreeBeforePostPruning, xgDataTest, xgLabelTest, xgName)
createPlot(convertTree(xgTreeBeforePostPruning))
createPlot(xgTreePostPruning)
结果:
四、总结
对比预剪枝与后剪枝生成的决策树,可以看出,后剪枝通常比预剪枝保留更多的分支,其欠拟合风险很小,因此后剪枝的泛化性能往往由于预剪枝决策树。但后剪枝过程是从底往上裁剪,因此其训练时间开销比前剪枝要大。文章来源地址https://www.toymoban.com/news/detail-460949.html
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