决策树系列三——基尼指数，减枝和

Posted 2020-11-30 131415-520

-- coding: utf-8 --

"""
Created on Tue Aug 14 17:36:57 2018

@author: weixw
"""
import numpy as np

定义树结构，采用的二叉树，左子树：条件为true，右子树：条件为false

leftBranch:左子树结点

rightBranch:右子树结点

col:信息增益最大时对应的列索引

value:最优列索引下，划分数据类型的值

results:分类结果

summary:信息增益最大时样本信息

data:信息增益最大时数据集

class Tree:
def init(self, leftBranch=None, rightBranch=None, col=-1, value=None, results=None, summary=None, data=None):
self.leftBranch = leftBranch
self.rightBranch = rightBranch
self.col = col
self.value = value
self.results = results
self.summary = summary
self.data = data

def __str__(self):
    print(u"列号：%d" % self.col)
    print(u"列划分值：%s" % self.value)
    print(u"样本信息：%s" % self.summary)
    return ""

划分数据集

def splitDataSet(dataSet, value, column):
leftList = []
rightList = []
# 判断value是否是数值型
if (isinstance(value, int) or isinstance(value, float)):
# 遍历每一行数据
for rowData in dataSet:
# 如果某一行指定列值>=value，则将该行数据保存在leftList中，否则保存在rightList中
if (rowData[column] >= value):
leftList.append(rowData)
else:
rightList.append(rowData)
# value为标称型
else:
# 遍历每一行数据
for rowData in dataSet:
# 如果某一行指定列值==value，则将该行数据保存在leftList中，否则保存在rightList中
if (rowData[column] == value):
leftList.append(rowData)
else:
rightList.append(rowData)
return leftList, rightList

统计标签类每个样本个数

‘‘‘
该函数是计算gini值的辅助函数，假设输入的dataSet为为[‘A‘, ‘B‘, ‘C‘, ‘A‘, ‘A‘, ‘D‘]，
则输出为[‘A‘:3,‘ B‘:1, ‘C‘:1, ‘D‘:1]，这样分类统计dataSet中每个类别的数量
‘‘‘

def calculateDiffCount(dataSet):
results = {}
for data in dataSet:
# data[-1] 是数据集最后一列，也就是标签类
if data[-1] not in results:
results.setdefault(data[-1], 1)
else:
results[data[-1]] += 1
return results

基尼指数公式实现

def gini(dataSet):
# 计算gini的值(Calculate GINI)
# 数据所有行
length = len(dataSet)
# 标签列合并后的数据集
results = calculateDiffCount(dataSet)
imp = 0.0
for i in results:
imp += results[i] / length * results[i] / length
return 1 - imp

生成决策树

‘‘‘算法步骤‘‘‘
‘‘‘根据训练数据集，从根结点开始，递归地对每个结点进行以下操作，构建二叉决策树：
1 设结点的训练数据集为D，计算现有特征对该数据集的信息增益。此时，对每一个特征A，对其可能取的
每个值a，根据样本点对A >=a 的测试为“是”或“否”将D分割成D1和D2两部分，利用基尼指数计算信息增益。
2 在所有可能的特征A以及它们所有可能的切分点a中，选择信息增益最大的特征及其对应的切分点作为最优特征
与最优切分点，依据最优特征与最优切分点，从现结点生成两个子结点，将训练数据集依特征分配到两个子结点中去。
3 对两个子结点递归地调用1,2，直至满足停止条件。
4 生成CART决策树。
‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘‘

evaluationFunc= gini :采用的是基尼指数来衡量信息关注度

def buildDecisionTree(dataSet, evaluationFunc=gini):
# 计算基础数据集的基尼指数
baseGain = evaluationFunc(dataSet)
# 计算每一行的长度（也就是列总数）
columnLength = len(dataSet[0])
# 计算数据项总数
rowLength = len(dataSet)
# 初始化
bestGain = 0.0 # 信息增益最大值
bestValue = None # 信息增益最大时的列索引，以及划分数据集的样本值
bestSet = None # 信息增益最大，听过样本值划分数据集后的数据子集
# 标签列除外（最后一列），遍历每一列数据
for col in range(columnLength - 1):
# 获取指定列数据
colSet = [example[col] for example in dataSet]
# 获取指定列样本唯一值
uniqueColSet = set(colSet)
# 遍历指定列样本集
for value in uniqueColSet:
# 分割数据集
leftDataSet, rightDataSet = splitDataSet(dataSet, value, col)
# 计算子数据集概率，python3 "/"除号结果为小数
prop = len(leftDataSet) / rowLength
# 计算信息增益
infoGain = baseGain - prop * evaluationFunc(leftDataSet) - (1 - prop) * evaluationFunc(rightDataSet)
# 找出信息增益最大时的列索引，value,数据子集
if (infoGain > bestGain):
bestGain = infoGain
bestValue = (col, value)
bestSet = (leftDataSet, rightDataSet)
# 结点信息
# nodeDescription = {‘impurity:%.3f‘%baseGain,‘sample:%d‘%rowLength}
nodeDescription = {‘impurity‘: ‘%.3f‘ % baseGain, ‘sample‘: ‘%d‘ % rowLength}
# 数据行标签类别不一致，可以继续分类
# 递归必须有终止条件
if bestGain > 0:
# 递归，生成左子树结点，右子树结点
leftBranch = buildDecisionTree(bestSet[0], evaluationFunc)
rightBranch = buildDecisionTree(bestSet[1], evaluationFunc)
return Tree(leftBranch=leftBranch, rightBranch=rightBranch, col=bestValue[0]
, value=bestValue[1], summary=nodeDescription, data=bestSet)
else:
# 数据行标签类别都相同，分类终止
return Tree(results=calculateDiffCount(dataSet), summary=nodeDescription, data=dataSet)

def createTree(dataSet, evaluationFunc=gini):
# 递归建立决策树， 当gain=0，时停止回归
# 计算基础数据集的基尼指数
baseGain = evaluationFunc(dataSet)
# 计算每一行的长度（也就是列总数）
columnLength = len(dataSet[0])
# 计算数据项总数
rowLength = len(dataSet)
# 初始化
bestGain = 0.0 # 信息增益最大值
bestValue = None # 信息增益最大时的列索引，以及划分数据集的样本值
bestSet = None # 信息增益最大，听过样本值划分数据集后的数据子集
# 标签列除外（最后一列），遍历每一列数据
for col in range(columnLength - 1):
# 获取指定列数据
colSet = [example[col] for example in dataSet]
# 获取指定列样本唯一值
uniqueColSet = set(colSet)
# 遍历指定列样本集
for value in uniqueColSet:
# 分割数据集
leftDataSet, rightDataSet = splitDataSet(dataSet, value, col)
# 计算子数据集概率，python3 "/"除号结果为小数
prop = len(leftDataSet) / rowLength
# 计算信息增益
infoGain = baseGain - prop * evaluationFunc(leftDataSet) - (1 - prop) * evaluationFunc(rightDataSet)
# 找出信息增益最大时的列索引，value,数据子集
if (infoGain > bestGain):
bestGain = infoGain
bestValue = (col, value)
bestSet = (leftDataSet, rightDataSet)

impurity = u'%.3f' % baseGain
sample = '%d' % rowLength

if bestGain > 0:
    bestFeatLabel = u'serial:%s
impurity:%s
sample:%s' % (bestValue[0], impurity, sample)
    myTree = {bestFeatLabel: {}}
    myTree[bestFeatLabel][bestValue[1]] = createTree(bestSet[0], evaluationFunc)
    myTree[bestFeatLabel]['no'] = createTree(bestSet[1], evaluationFunc)
    return myTree
else:  # 递归需要返回值
    bestFeatValue = u'%s
impurity:%s
sample:%s' % (str(calculateDiffCount(dataSet)), impurity, sample)
    return bestFeatValue

分类测试：

‘‘‘根据给定测试数据遍历二叉树，找到符合条件的叶子结点‘‘‘
‘‘‘例如测试数据为[5.9,3,4.2,1.75]，按照训练数据生成的决策树分类的顺序为
第2列对应测试数据4.2 =>与决策树根结点（2）的value（3）比较，>=3则遍历左子树，否则遍历右子树，
叶子结点就是结果‘‘‘

def classify(data, tree):
# 判断是否是叶子结点，是就返回叶子结点相关信息，否就继续遍历
if tree.results != None:
return u"%s %s" % (tree.results, tree.summary)
else:
branch = None
v = data[tree.col]
# 数值型数据
if isinstance(v, int) or isinstance(v, float):
if v >= tree.value:
branch = tree.leftBranch
else:
branch = tree.rightBranch
else: # 标称型数据
if v == tree.value:
branch = tree.leftBranch
else:
branch = tree.rightBranch
return classify(data, branch)

def loadCSV(fileName):
def convertTypes(s):
s = s.strip()
try:
return float(s) if ‘.‘ in s else int(s)
except ValueError:
return s

data = np.loadtxt(fileName, dtype='str', delimiter=',')
data = data[1:, :]
dataSet = ([[convertTypes(item) for item in row] for row in data])
return dataSet

多数表决器

列中相同值数量最多为结果

def majorityCnt(classList):
import operator
classCounts = {}
for value in classList:
if (value not in classCounts.keys()):
classCounts[value] = 0
classCounts[value] += 1
sortedClassCount = sorted(classCounts.items(), key=operator.itemgetter(1), reverse=True)
return sortedClassCount[0][0]

剪枝算法(前序遍历方式：根=>左子树=>右子树)

‘‘‘算法步骤

1. 从二叉树的根结点出发，递归调用剪枝算法，直至左、右结点都是叶子结点
2. 计算父节点（子结点为叶子结点）的信息增益infoGain
3. 如果infoGain < miniGain，则选取样本多的叶子结点来取代父节点
4. 循环1,2,3，直至遍历完整棵树
   ‘‘‘‘‘‘‘‘‘

def prune(tree, miniGain, evaluationFunc=gini):
print(u"当前结点信息:")
print(str(tree))
# 如果当前结点的左子树不是叶子结点，遍历左子树
if (tree.leftBranch.results == None):
print(u"左子树结点信息:")
print(str(tree.leftBranch))
prune(tree.leftBranch, miniGain, evaluationFunc)
# 如果当前结点的右子树不是叶子结点，遍历右子树
if (tree.rightBranch.results == None):
print(u"右子树结点信息:")
print(str(tree.rightBranch))
prune(tree.rightBranch, miniGain, evaluationFunc)
# 左子树和右子树都是叶子结点
if (tree.leftBranch.results != None and tree.rightBranch.results != None):
# 计算左叶子结点数据长度
leftLen = len(tree.leftBranch.data)
# 计算右叶子结点数据长度
rightLen = len(tree.rightBranch.data)
# 计算左叶子结点概率
leftProp = leftLen / (leftLen + rightLen)
# 计算该结点的信息增益（子类是叶子结点）
infoGain = (evaluationFunc(tree.leftBranch.data + tree.rightBranch.data) -
leftProp * evaluationFunc(tree.leftBranch.data) - (1 - leftProp) * evaluationFunc(
tree.rightBranch.data))
# 信息增益 < 给定阈值，则说明叶子结点与其父结点特征差别不大，可以剪枝
if (infoGain < miniGain):
# 合并左右叶子结点数据
dataSet = tree.leftBranch.data + tree.rightBranch.data
# 获取标签列
classLabels = [example[-1] for example in dataSet]
# 找到样本最多的标签值
keyLabel = majorityCnt(classLabels)
# 判断标签值是左右叶子结点哪一个
if keyLabel in tree.leftBranch.results:
# 左叶子结点取代父结点
tree.data = tree.leftBranch.data
tree.results = tree.leftBranch.results
tree.summary = tree.leftBranch.summary
else:
# 右叶子结点取代父结点
tree.data = tree.rightBranch.data
tree.results = tree.rightBranch.results
tree.summary = tree.rightBranch.summary
tree.leftBranch = None
tree.rightBranch = None

‘‘‘
Created on Oct 14, 2010

@author: Peter Harrington
‘‘‘
import matplotlib.pyplot as plt

decisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="circle", fc="0.7")
arrow_args = dict(arrowstyle="<-")

获取树的叶子节点

def getNumLeafs(myTree):
numLeafs = 0
#dict转化为list
firstSides = list(myTree.keys())
firstStr = firstSides[0]
secondDict = myTree[firstStr]
for key in secondDict.keys():
#判断是否是叶子节点（通过类型判断，子类不存在，则类型为str；子类存在，则为dict）
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

获取树的层数

def getTreeDepth(myTree):
maxDepth = 0
#dict转化为list
firstSides = list(myTree.keys())
firstStr = firstSides[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)
firstSides = list(myTree.keys())
firstStr = firstSides[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

if you do get a dictonary you know it‘s a tree, and the first element will be another dict

绘制决策树 样例1

def createPlot(inTree):
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
#宽，高间距
plotTree.totalW = float(getNumLeafs(inTree))-3
plotTree.totalD = float(getTreeDepth(inTree))-2

plotTree.totalW = float(getNumLeafs(inTree))

plotTree.totalD = float(getTreeDepth(inTree))

plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0;
plotTree(inTree, (0.95,1.0), '')
plt.show()

绘制决策树 样例2

def createPlot1(inTree):
fig = plt.figure(1, facecolor=‘white‘)
# fig = plt.figure(dpi=255)
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
#宽，高间距
plotTree.totalW = float(getNumLeafs(inTree))-4.5
plotTree.totalD = float(getTreeDepth(inTree)) -3
plotTree.xOff = -0.5/plotTree.totalW; plotTree.yOff = 1.0;
plotTree(inTree, (1.0,1.0), ‘‘)
plt.show()

绘制树的根节点和叶子节点（根节点形状：长方形，叶子节点：椭圆形）

def createPlot():

fig = plt.figure(1, facecolor=‘white‘)

fig.clf()

createPlot.ax1 = plt.subplot(111, frameon=False) #ticks for demo puropses

plotNode(‘a decision node‘, (0.5, 0.1), (0.1, 0.5), decisionNode)

plotNode(‘a leaf node‘, (0.8, 0.1), (0.3, 0.8), leafNode)

plt.show()

def retrieveTree(i):
listOfTrees =[{‘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 listOfTrees[i]

thisTree = retrieveTree(0)

createPlot(thisTree)

createPlot()

myTree = retrieveTree(0)

numLeafs =getNumLeafs(myTree)

treeDepth =getTreeDepth(myTree)

print(u"叶子节点数目：%d"% numLeafs)

print(u"树深度：%d"%treeDepth)

-- coding: utf-8 --

"""
Created on Wed Aug 15 14:16:59 2018

@author: weixw
"""
import Demo_1.myCart as mc
from Demo_1.myCart import gini
if name == ‘main‘:
import treePlotter as tp
dataSet = mc.loadCSV("F:C盘移过来的文件dataSet.csv")
myTree = mc.createTree(dataSet, evaluationFunc=gini)
print(u"myTree:%s"%myTree)
#绘制决策树
print(u"绘制决策树：")
tp.createPlot1(myTree)
decisionTree = mc.buildDecisionTree(dataSet, evaluationFunc=gini)
testData = [5.9,3,4.2,1.75]
r = mc.classify(testData, decisionTree)
print(u"分类后测试结果:")
print(r)
print()
mc.prune(decisionTree, 0.4)
r1 = mc.classify(testData, decisionTree)
print(u"剪枝后测试结果:")
print(r1)