机器学习基础决策树分类

决策树就是通过一系列条件判断分类的方法

#encoding: utf-8
from math import log
import operator
#两个文件相互import会出错，具体参考http://blog.csdn.net/sinat_16790541/article/details/43376741
#import TreePlotter
import pickle #用于序列化对象并且在磁盘上存储

def calcShannonEnt(dataSet):
numEntries = len(dataSet)
labelCounts = {}
#为所有可能分类创造字典
for featVec in dataSet:
currentLabel = featVec[-1] #键值是最后一列的数值
if currentLabel not in labelCounts.keys():
labelCounts[currentLabel] = 0
labelCounts[currentLabel] += 1
#计算香农熵
shannonEnt = 0.0
for key in labelCounts:
prob = float(labelCounts[key]) / numEntries #所有类出现的频率
shannonEnt -= prob * log(prob, 2) # H=∑ p[i]*log(p[i],2)
return shannonEnt

#自定义数据
def createDataSet():
dataSet = [[1, 1, 'yes'], [1, 1, 'yes'], [0, 1, 'no'], [1, 0, 'no'],
[0, 1, 'no']]
labels = ['no surfacing', 'flippers']
return dataSet, labels

#按照给定特征划分数据集，参数：待划分数据集，划分数据集的特征的位置，需要返回的特征的值
def splitDataSet(dataSet, axis, value):
retDateSet = [] #新的list对象，避免修改dataSet
for featVec in dataSet:
if featVec[axis] == value:
#抽取符合的元素,去掉用作特征的元素
reducedFeatVec = featVec[:axis]
#extend()函數合併添加列表元素
reducedFeatVec.extend(featVec[axis + 1:])
#append()函數添加第四個元素，列表
retDateSet.append(reducedFeatVec)
return retDateSet

#选择最好的数据集划分方式
def chooseBestFeatureToSplit(dataSet):
#在第一行计算特征的数量
numFeatures = len(dataSet[0]) - 1
#计算初始信息熵
baseEntropy = calcShannonEnt(dataSet)
bestInfoGain = 0.0
bestFeature = -1
for i in range(numFeatures):
#创建唯一的分类标签
featList = [example[i] for example in dataSet]
#set集合中元素互不相同
uniqueVals = set(featList)
newEntropy = 0.0
#计算每种划分方式的信息熵
for value in uniqueVals:
subDataSet = splitDataSet(dataSet, i, value)
prob = len(subDataSet) / float(len(dataSet))
newEntropy += prob * calcShannonEnt(subDataSet)
infoGain = baseEntropy - newEntropy
#计算最好的信息增益
if (infoGain > bestInfoGain):
bestInfoGain = infoGain
bestFeature = i
return bestFeature

#返回出现次数最多的分类名称
def majorityCnt(classList):
classCount = {}
for vote in classList:
if vote not in classCount.keys():
classCount[vote] = 0
classCount[vote] += 1
sortedClassCount = sorted(
classCount.items(), key=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]

#递归建树，参数为数据集和标签列表
def createTree(dataSet, labels):
classList = [example[-1] for example in dataSet]
#类别完全相同时停止划分
if classList.count(classList[0]) == len(classList):
return classList[0]
#便利完所有特征时返回出现次数最多的类别
if len(dataSet[0]) == 1:
return majorityCnt(classList)
#当前数据集选取的最好特征
bestFeat = chooseBestFeatureToSplit(dataSet)
bestFeatLabel = labels[bestFeat]
myTree = {bestFeatLabel: {}}
del (labels[bestFeat])
#得到列表包含的所有属性值
featValues = [example[bestFeat] for example in dataSet]
uniqueVals = set(featValues)
#递归建树
for value in uniqueVals:
#函数参数是列表类型时，参数按引用方式传递，所以采用新变量代替原始列表
subLabels = labels[:]
myTree[bestFeatLabel][value] = createTree(
splitDataSet(dataSet, bestFeat, value), subLabels)
return myTree

def classify(inputTree, featLabels, testVec):
firstStr = list(inputTree.keys())[0]
secondDict = inputTree[firstStr]
#将标签字符串转换为索引
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

#利用pickle包存储树，减少后续计算时间
def storeTree(inputTree, filename):
##读写模式:r只读,r+读写,w新建(会覆盖原有文件),a追加,b二进制文件.常用模式
#pickle存储方式默认是二进制方式，所以读写方式要加b
fw = open(filename, 'wb+')
pickle.dump(inputTree, fw)
fw.close

def grabTree(filename):
fr = open(filename, 'rb+')
return pickle.load(fr)

'''
mydat, labels = createDataSet()
print(mydat)
print(labels)

print(calcShannonEnt(mydat))
print(splitDataSet(mydat, 0, 1))
print(chooseBestFeatureToSplit(mydat))
myTree = createTree(mydat, labels)

myTree = TreePlotter.retrieveTree(0)
print(myTree)
storeTree(myTree, 'classifierStorage.txt')
print(grabTree('classifierStorage.txt'))
print(classify(myTree, labels, [1, 1]))
'''

采用matplotlib来绘制属树形图
#encoding: utf-8
import matplotlib.pyplot as plt
import Trees

#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='<-')

#绘制带箭头的注解
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 createPlot(inTree):
fig = plt.figure(1, facecolor='white')
fig.clf()
#定义绘图区,绘制图形的X轴和Y轴的有效范围都是0.0~1.0
axprops = dict(xticks=[], yticks=[])
createPlot.ax1 = plt.subplot(111, frameon=False, **axprops)
#记录树的宽度和深度
plotTree.totalW = float(getNumLeafs(inTree))
plotTree.totalD = float(getTreeDepth(inTree))
#分号使用在把多个简单语句（比如赋值语句，print，函数调用）放在同一行的时候，使用分号把它们隔开
plotTree.xOff = -0.5 / plotTree.totalW
plotTree.yOff = 1.0
plotTree(inTree, (0.5, 1.0), '')
plt.show()
'''
plotNode('judge', (0.5, 0.1), (0.1, 0.5), decisionNode)
plotNode('leaf', (0.8, 0.1), (0.3, 0.8), leafNode)
'''

#求叶节点数目
def getNumLeafs(myTree):
numLeafs = 0
firstStr = list(myTree.keys())[0]
secondDict = myTree[firstStr]
for key in secondDict.keys():
#测试节点的数据类型是否还是字典
if type(secondDict[key]).__name__ == 'dict':
numLeafs += getNumLeafs(secondDict[key])
else:
numLeafs += 1
return numLeafs

#求树的深度
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

#在父子节点之间填充文本信息
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, parentPt, nodeText):
#计算宽和高
numLeafs = getNumLeafs(myTree)
depth = getTreeDepth(myTree)
firstStr = list(myTree.keys())[0]
cntrPt = (plotTree.xOff + (1.0 + float(numLeafs)) / 2.0 / plotTree.totalW,
plotTree.yOff)
#标记子节点属性值
plotMidText(cntrPt, parentPt, nodeText)
plotNode(firstStr, cntrPt, parentPt, decisionNode)
secondDict = myTree[firstStr]
#减少y的偏移量
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

#预先存储树的信息避免每次测试的时候都要建树
def retrieveTree(i):
listOfTree = [{
'no surfacing': {
0: 'no',
1: {
'flippers': {
0: 'no',
1: 'yes'
}
}
}
}, {
'no surfacing': {
0: 'no',
1: {
'flippers': {
0: {
'head': {
0: 'no',
1: 'yes'
}
},
1: 'no'
}
}
}
}]
return listOfTree[i]

'''
#createPlot()
myTree = retrieveTree(0)
myTree['no surfacing'][3]='maybe'
print(myTree)
createPlot(myTree)
'''
fr = open('lenses.txt','r+')
#readlines()读取整个文件所有行，保存在一个列表(list)变量中，每行作为一个元素
lenses=[inst.strip().split('\t') for inst in fr.readlines()]
lensesLabels=['age','prescript','astigmatic','tearRate']
lensesTree=Trees.createTree(lenses,lensesLabels)
createPlot(lensesTree)