python实现ID3决策树算法

ID3决策树是以信息增益作为决策标准的一种贪心决策树算法

# -*- coding: utf-8 -*-


from numpy import *
import math
import copy
import cPickle as pickle


class ID3DTree(object):
  def __init__(self): # 构造方法
    self.tree = {} # 生成树
    self.dataSet = [] # 数据集
    self.labels = [] # 标签集


  # 数据导入函数
  def loadDataSet(self, path, labels):
    recordList = []
    fp = open(path, "rb") # 读取文件内容
    content = fp.read()
    fp.close()
    rowList = content.splitlines() # 按行转换为一维表
    recordList = [row.split("\t") for row in rowList if row.strip()] # strip()函数删除空格、Tab等
    self.dataSet = recordList
    self.labels = labels


  # 执行决策树函数
  def train(self):
    labels = copy.deepcopy(self.labels)
    self.tree = self.buildTree(self.dataSet, labels)


  # 构件决策树：穿件决策树主程序
  def buildTree(self, dataSet, lables):
    cateList = [data[-1] for data in dataSet] # 抽取源数据集中的决策标签列
    # 程序终止条件1：如果classList只有一种决策标签，停止划分，返回这个决策标签
    if cateList.count(cateList[0]) == len(cateList):
      return cateList[0]
    # 程序终止条件2：如果数据集的第一个决策标签只有一个，返回这个标签
    if len(dataSet[0]) == 1:
      return self.maxCate(cateList)
    # 核心部分
    bestFeat = self.getBestFeat(dataSet) # 返回数据集的最优特征轴
    bestFeatLabel = lables[bestFeat]
    tree = {bestFeatLabel: {}}
    del (lables[bestFeat])
    # 抽取最优特征轴的列向量
    uniqueVals = set([data[bestFeat] for data in dataSet]) # 去重
    for value in uniqueVals: # 决策树递归生长
      subLables = lables[:] # 将删除后的特征类别集建立子类别集
      # 按最优特征列和值分隔数据集
      splitDataset = self.splitDataSet(dataSet, bestFeat, value)
      subTree = self.buildTree(splitDataset, subLables) # 构建子树
      tree[bestFeatLabel][value] = subTree
    return tree


  # 计算出现次数最多的类别标签
  def maxCate(self, cateList):
    items = dict([(cateList.count(i), i) for i in cateList])
    return items[max(items.keys())]


  # 计算最优特征
  def getBestFeat(self, dataSet):
    # 计算特征向量维，其中最后一列用于类别标签
    numFeatures = len(dataSet[0]) - 1 # 特征向量维数=行向量维数-1
    baseEntropy = self.computeEntropy(dataSet) # 基础熵
    bestInfoGain = 0.0 # 初始化最优的信息增益
    bestFeature = -1 # 初始化最优的特征轴
    # 外循环：遍历数据集各列，计算最优特征轴
    # i为数据集列索引：取值范围0~(numFeatures-1)
    for i in xrange(numFeatures):
      uniqueVals = set([data[i] for data in dataSet]) # 去重
      newEntropy = 0.0
      for value in uniqueVals:
        subDataSet = self.splitDataSet(dataSet, i, value)
        prob = len(subDataSet) / float(len(dataSet))
        newEntropy += prob * self.computeEntropy(subDataSet)
      infoGain = baseEntropy - newEntropy
      if (infoGain > bestInfoGain): # 信息增益大于0
        bestInfoGain = infoGain # 用当前信息增益值替代之前的最优增益值
        bestFeature = i # 重置最优特征为当前列
    return bestFeature



  # 计算信息熵
  # @staticmethod
  def computeEntropy(self, dataSet):
    dataLen = float(len(dataSet))
    cateList = [data[-1] for data in dataSet] # 从数据集中得到类别标签
    # 得到类别为key、 出现次数value的字典
    items = dict([(i, cateList.count(i)) for i in cateList])
    infoEntropy = 0.0
    for key in items: # 香农熵： = -p*log2(p) --infoEntropy = -prob * log(prob, 2)
      prob = float(items[key]) / dataLen
      infoEntropy -= prob * math.log(prob, 2)
    return infoEntropy


  # 划分数据集： 分割数据集； 删除特征轴所在的数据列，返回剩余的数据集
  # dataSet : 数据集； axis: 特征轴； value: 特征轴的取值
  def splitDataSet(self, dataSet, axis, value):
    rtnList = []
    for featVec in dataSet:
      if featVec[axis] == value:
        rFeatVec = featVec[:axis] # list操作：提取0~（axis-1）的元素
        rFeatVec.extend(featVec[axis + 1:])
        rtnList.append(rFeatVec)
    return rtnList
  # 存取树到文件
  def storetree(self, inputTree, filename):
    fw = open(filename,'w')
    pickle.dump(inputTree, fw)
    fw.close()

  # 从文件抓取树
  def grabTree(self, filename):
    fr = open(filename)
    return pickle.load(fr)

调用代码

# -*- coding: utf-8 -*-

from numpy import *
from ID3DTree import *

dtree = ID3DTree()
# ["age", "revenue", "student", "credit"]对应年龄、收入、学生、信誉4个特征
dtree.loadDataSet("dataset.dat", ["age", "revenue", "student", "credit"])
dtree.train()

dtree.storetree(dtree.tree, "data.tree")
mytree = dtree.grabTree("data.tree")
print mytree

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