# 计算给定数据集的香农熵
from math import log
def calcShannonEnt(dataSet):
numEntries = len(dataSet)
labelCounts = {}
for featVec in dataSet: #the the number of unique elements and their occurance
currentLabel = featVec[-1]
if currentLabel not in labelCounts.keys(): labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
shannonEnt = 0.0
for key in labelCounts:
prob = float(labelCounts[key])/numEntries
shannonEnt -= prob * log(prob,2) #log base 2
return shannonEnt
def createDataSet():
dataSet = [[1, 1, 'yes'],
[1, 1, 'yes'],
[1, 0, 'no'],
[0, 1, 'no'],
[0, 1, 'no']]
labels = ['no surfacing', 'flippers']
return dataSet, labels
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
calcShannonEnt(myDat)
0.9709505944546686
熵越高,则混合的数据也越多,我们可以在数据集中添加更多的分类,观察熵是如何变化的。这里我们增加第三个名为maybe的分类, 测试熵的变化:
myDat[0][-1] = 'maybe'
calcShannonEnt(myDat)
1.3709505944546687
# 按照给定特征划分数据集
# /*
# * dataSet: 待划分的数据集
# * axis: 划分数据的特征
# * 需要返回的特征的值
# */
def splitDataSet(dataSet, axis, value):
retDataSet = []
for featVec in dataSet:
if featVec[axis] == value:
reducedFeatVec = featVec[:axis] #chop out axis used for splitting
reducedFeatVec.extend(featVec[axis+1:])
retDataSet.append(reducedFeatVec)
return retDataSet
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
splitDateSet(myDat, 0, 1) # 以第一个特征,特征值为1划分的结果
[[1, 'yes'], [1, 'yes'], [0, 'no']]
splitDateSet(myDat, 0, 0) # 以第一个特征,特征值为0划分的结果
[[1, 'no'], [1, 'no']]
# 选择最好的数据集划分方式
def chooseBestFeatureToSplit(dataSet):
numFeatures = len(dataSet[0]) - 1 #the last column is used for the labels
baseEntropy = calcShannonEnt(dataSet)
bestInfoGain = 0.0; bestFeature = -1
for i in range(numFeatures): #iterate over all the features
featList = [example[i] for example in dataSet]#create a list of all the examples of this feature
uniqueVals = set(featList) #get a set of unique values
newEntropy = 0.0
for value in uniqueVals:
subDataSet = splitDataSet(dataSet, i, value)
prob = len(subDataSet)/float(len(dataSet))
newEntropy += prob * calcShannonEnt(subDataSet)
infoGain = baseEntropy - newEntropy #calculate the info gain; ie reduction in entropy
if (infoGain > bestInfoGain): #compare this to the best gain so far
bestInfoGain = infoGain #if better than current best, set to best
bestFeature = i
return bestFeature #returns an integer
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
bestFeature = chooseBestFeatureToSplit(myDat)
print("bestFeature is {}".format(bestFeature))
bestFeature is 0
# 多数表决决定该叶子节点分类
import operator
def majorityCnt(classList):
classCount = {}
for vote in classList:
if vote not in classCount.keys():
classCount[vote] = 0
classCount[vote] += 1
sortedClassCount = sorted(classCount.iteritems(), key=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]
# 创建树的函数代码
def createTree(dataSet,labels):
classList = [example[-1] for example in dataSet]
if classList.count(classList[0]) == len(classList):
return classList[0]#stop splitting when all of the classes are equal
if len(dataSet[0]) == 1: #stop splitting when there are no more features in dataSet
return majorityCnt(classList)
bestFeat = chooseBestFeatureToSplit(dataSet)
bestFeatLabel = labels[bestFeat]
myTree = {bestFeatLabel:{}}
del(labels[bestFeat])
featValues = [example[bestFeat] for example in dataSet]
uniqueVals = set(featValues)
for value in uniqueVals:
subLabels = labels[:] #copy all of labels, so trees don't mess up existing labels
myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
return myTree
myDat, labels = createDataSet()
myDat
[[1, 1, 'yes'], [1, 1, 'yes'], [1, 0, 'no'], [0, 1, 'no'], [0, 1, 'no']]
createTree(myDat, labels)
{'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}}
Matplotlib提供了一个非常有用的注解工具annotations
# 使用文本注解绘制树节点
import matplotlib.pyplot as plt
#解决中文显示问题
plt.rcParams['font.sans-serif']=['SimHei']
plt.rcParams['axes.unicode_minus'] = False
decisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
arrow_args = dict(arrowstyle='<-')
def plotNode(nodeText, centerPt, parentPt, nodeType):
createPlot.ax1.annotate(nodeText, xy=parentPt, xycoords='axes fraction',
xytext=centerPt, textcoords="axes fraction",
va="center", ha="center", bbox=nodeType, arrowprops=arrow_args)
def createPlot():
fig =plt.figure(1, facecolor="white")
fig.clf()
createPlot.ax1 = plt.subplot(111, frameon=False)
plotNode('决策节点', (0.5, 0.1), (0.1, 0.5), decisionNode)
plotNode('叶节点', (0.8, 0.1), (0.3, 0.8), leafNode)
plt.show()
createPlot()
# 获取叶节点的数目和数的层数
def getNumLeafs(myTree):
numLeafs = 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 retrieveTree(i):
listOfTrees = [{'flippers': {0: 'no', 1: {'no surfacing': {0: 'no', 1: 'yes'}}}},
{'flippers': {0: 'no', 1: {'no surfacing': {0: {'head':{0: 'no', 1:'yes'}}, 1: 'yes'}}}}]
return listOfTrees[i]
retrieveTree(1)
{'flippers': {0: 'no',
1: {'no surfacing': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'yes'}}}}
myTree = retrieveTree(0)
getNumLeafs(myTree)
3
getTreeDepth(myTree)
2
# plotTree函数
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)
def plotTree(myTree, parentPr, 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, parentPr, nodeTxt)
plotNode(firstStr, cntrpt, parentPr, 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.ax1 = 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()
myTree = retrieveTree(1)
createPlot(myTree)
myTree['flippers'][0] = 'maybe'
createPlot(myTree)
# 使用决策树的分类函数
def classify(inputTree, featLabels, testVec):
firstStr = list(inputTree.keys())[0]
secondDict = inputTree[firstStr]
featIndex = featLabels.index(firstStr)
for key in secondDict.keys():
if testVec[featIndex] == key:
if type(secondDict[key]).__name__ == 'dict':
classLabel = classify(secondDict[key], featLabels, testVec)
else:
classLabel = secondDict[key]
return classLabel
myDat, labels = createDataSet()
labels
['no surfacing', 'flippers']
myTree = retrieveTree(0)
myTree
{'flippers': {0: 'no', 1: {'no surfacing': {0: 'no', 1: 'yes'}}}}
classify(myTree, labels, [1, 0])
'no'
classify(myTree, labels, [1, 1])
'yes'
# 使用pickle模块存储决策树
def storeTree(inputTree, filename):
import pickle
fw = open(filename, 'wb')
pickle.dump(inputTree, fw)
fw.close()
def grabTree(filename):
import pickle
fr = open(filename, 'rb')
return pickle.load(fr)
myTree
{'flippers': {0: 'no', 1: {'no surfacing': {0: 'no', 1: 'yes'}}}}
storeTree(myTree, 'data/classifierStorage.txt')
grabTree('data/classifierStorage.txt')
{'flippers': {0: 'no', 1: {'no surfacing': {0: 'no', 1: 'yes'}}}}
data = open('data/lenses.txt')
lenses = [inst.strip().split('\t') for inst in data.readlines()]
lensesLabels = ['age', 'prescript', 'astigmatic', 'tearRate']
lensesTree = createTree(lenses, lensesLabels)
lensesTree
{'tearRate': {'normal': {'astigmatic': {'no': {'age': {'pre': 'soft',
'presbyopic': {'prescript': {'hyper': 'soft', 'myope': 'no lenses'}},
'young': 'soft'}},
'yes': {'prescript': {'hyper': {'age': {'pre': 'no lenses',
'presbyopic': 'no lenses',
'young': 'hard'}},
'myope': 'hard'}}}},
'reduced': 'no lenses'}}
createPlot(lensesTree)