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决策树原理
决策树是一种从训练数据中学习得出一个树状结构的模型。这种模型属于判别模型。决策树是一种树状结构，通过做出一系列决策来对数据进行划分，这类似针对一系列问题进行选择。决策树的决策过程就是从根结点开始，测试待分类项中对应的特征属性，并按照其值选择输出分支，直到叶子节点，最后将叶子节点的存放的类别作为决策结果。
决策树算法是一种归纳分类算法 ，它通过对训练集的学习，挖掘 出有用的规则，用于对新数据进 行预测。决策树归纳的基本算法是贪心算法 ，自顶向下来构建决策树。每一步选择中都采取在当前状态下最好的算法。在决策树生成过程中，属性选择度量是关机。
决策树算法之一（ID3算法）
该算法支持分类模型，树结构为多叉数，通过信息增益进行特征选择，不支持连续值和缺失值处理，也不支持剪枝和特征属性多次使用。
ID3大致算法流程如下：
ID3算法也存在缺陷，ID3没有剪枝策略，容易过拟合；信息增益准则对可取值数目较多的特征有所偏好，类似“编号”的特征其信息增益接近于1；只能用于处理离散分布的特征；没有考虑缺失值。
ID3算法代码实现
所选取的数据集为看天气今天是否出门，训练完成后，将决策树绘制出来。
from math import log
import pandas as pd
import numpy as np
import operator
from matplotlib.font_manager import FontProperties
import matplotlib.pyplot as plt
path = 'D:\MachineL\TreeTest.csv'
df = pd.read_csv(path)
dataSet=[]
dataSet= np.array(df.loc[:,:])
print(dataSet)
labels = list(df.columns.values)
labels.pop()
print(labels)
def calcShannonEnt(dataSet):
numEntries = len(dataSet)
labelCounts = {}
for featVec in dataSet:
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)
return shannonEnt # 返回经验熵
def splitDataSet(dataSet, axis, value):
retDataSet = []
for featVec in dataSet:
if featVec[axis] == value:
reducedFeatVec = featVec
retDataSet.append(reducedFeatVec)
return retDataSet
def chooseBestFeatureToSplit(dataSet):
numFeatures = len(dataSet[0]) - 1
baseEntropy = calcShannonEnt(dataSet)
bestInfoGain = 0.0
bestFeature = -1
for i in range(numFeatures):
featList = [example[i] for example in dataSet]
uniqueVals = set(featList)
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
print("第%d个特征的增益为%.3f" % (i, infoGain))
if (infoGain > bestInfoGain):
bestInfoGain = infoGain
bestFeature = i
return bestFeature
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]
def createTree(dataSet, labels, featLabels):
# 取分类标签（yes or no）
classList = [example[-1] for example in dataSet]
if classList.count(classList[0]) == len(classList):
return classList[0]
if len(dataSet[0]) == 1:
return majorityCnt(classList)
bestFeat = chooseBestFeatureToSplit(dataSet)
bestFeatLabel = labels[bestFeat]
featLabels.append(bestFeatLabel)
myTree = {bestFeatLabel: {}}
featValues = [example[bestFeat] for example in dataSet]
uniqueVls = set(featValues)
for value in uniqueVls:
myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),
labels, featLabels)
return myTree
def getNumLeafs(myTree):
numLeafs = 0
firstStr = next(iter(myTree))
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):#获取决策树的层数
maxDepth = 0
firstStr = next(iter(
myTree))
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 plotNode(nodeTxt, centerPt, parentPt, nodeType):#绘制图像结点
arrow_args = dict(arrowstyle="<-")
font = FontProperties(fname=r"c:\windows\fonts\simsun.ttc", size=14)
createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction',
xytext=centerPt, textcoords='axes fraction',
va="center", ha="center", bbox=nodeType, arrowprops=arrow_args, FontProperties=font)
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):#生成决策树
decisionNode = dict(boxstyle="sawtooth", fc="0.8")
leafNode = dict(boxstyle="round4", fc="0.8")
numLeafs = getNumLeafs(myTree)
depth = getTreeDepth(myTree)
firstStr = next(iter(myTree))
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):#绘制决策树图像
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() # 显示绘制结果
featLabels = []
myTree = createTree(dataSet, labels, featLabels)
print(myTree)
createPlot(myTree)
最终决策树的可视化如下：
特征值的增益如下：
