决策树

最新推荐文章于 2025-03-27 21:16:50 发布

wwgavin

最新推荐文章于 2025-03-27 21:16:50 发布

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分类专栏：机器学习实战文章标签：决策树算法机器学习实战

本文链接：https://blog.youkuaiyun.com/u013538959/article/details/74222093

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本文介绍了决策树算法的优点、缺点及应用场景，并提供了详细的决策树构建伪代码。通过具体案例讲解了如何利用Python实现决策树算法，包括信息增益的计算、决策树的构建与可视化等关键步骤。

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决策树性质

优点：计算复杂度不高，输出结果易于理解，对中间值的缺失不敏感，可以处理不相关特征数据。
缺点：可能会产生过度匹配问题。
使用数据类型：数值型和标称型。

决策树伪代码

输入：训练集 $D=\{(x_1,y_1), (x_2,y_2), ... , (x_n,y_n)\}$
属性集 $A = \{a_1, a_2, ... ,a_d\}$
输出：以node为根结点的一颗决策树

过程：createBranch()
检测数据集中的每个子项是否属于同一分类：
  if so return 类标签;
  else
      寻找划分数据集的最好特征
      划分数据集
      创建分支节点
          for 每个划分的子集
              调用函数createBranch并增加返回结果到分支界结点中
      return 分支结点

几点说明

最好的特征是指使得当前数据集信息增益最大的特征。
一般而言，信息增益越大，则意味着使用属性a来进行划分所获得的“纯度提升”越大。
决策树算法有可能出现过拟合现象。

数据集

from http://archive.ics.uci.edu/ml/machine-learning-databases/lenses/lenses.names

Number of Instances: 24
Number of Attributes: 4 (all nominal)
Attribute Information:

age of the patient:

(1) young
(2) pre-presbyopic
(3) presbyopic
spectacle prescription:

(1) myope
(2) hypermetrope
astigmatic:

(1) no
(2) yes
tear production rate:

(1) reduced
(2) normal
Class Distribution:

hard contact lenses: 4
soft contact lenses: 5
no contact lenses: 15

决策树算法python实现

main.py

import trees
import treePlotter

fr = open('lenses.txt')
lenses = [inst.strip().split('\t') for inst in fr.readlines()]
lensesLabels = ['age', 'prescript', 'astigmatic', 'tearRate']
lensesTree = trees.createTree(lenses, lensesLabels)
treePlotter.createPlot(lensesTree)

trees.createTree

#input：DataSet, Attributes
#output；decision tree
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

trees.majorityCnt

#input：list
#output：the most frequent num in the list
#algorithm：hash
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]

trees.chooseBestFeatureToSplit

信息增益: $Gain(D,a) = Ent(D) - \sum_{v=1}^{V}\frac{|D^v|}{D}Ent(D^v)$
$D$ ：待划分的数据集合；
$a$ ：划分当前数据集的特征；
$V$ ：当前特征的离散取值个数。

#input: dataSet
#output: current bestFeature
#algorithm: find the feature with best information gain
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

trees.calcShannonEnt

信息熵: $Ent(D) = -\sum\limits_{k=1}^{|y|}p_k\log_2p_k$
$|y|$ : 数据集 $D$ 中，样本种类的个数。

#input: current dataSet
#output: the information gain of current dataSet
#algorithm: Ent(D)
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

trees.splitDataSet

假定离散属性 $a$ 有 $V$ 个可能的取值 ${a^1, a^2, ..., a^V}$ ，若使用 $a$ 来对样本集 $D$ 进行划分则会产生 $V$ 个分支结点，其中第 $v$ 个分支结点包含了 $D$ 中所有在属性 $a$ 上取值为 $a^V$ 的样本，记为 $D^v$ 。

'''
input: dataSet: the dataset we'll split;
       axis: the feature we'll split on;
       value: the value of the feature.
output: dataset splitting on a given feature.
'''
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