决策树——算法实现

分类树，特征的值和类标签都是离散值

1. 计算熵，选择最优分类特征
2. 对分类后的各个子集再进行计算熵，选择最优分类特征
3. 停止条件：分类后的所有数据集都属于同一类；没有可分的特征，选择数量最多的类作为预测类；

import numpy as np
import math
import operator


def createDataSet():
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing','flippers']
    #change to discrete values
    return dataSet, labels

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 * math.log(prob,2) #log base 2
    return shannonEnt

# dataSet,axis 是数据集的的特征索引，value是特征的值，返回的是除去特征使value的数据
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


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


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]  # 返回元组列表[(k,v)]


def createTree(dataSet,dataLabels):
    labels = dataLabels[:]
    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


def classify(inputTree, featLabels, testVec):
    firstStr = list(inputTree.keys())[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)
    key = testVec[featIndex]
    valueOfFeat = secondDict[key]
    if isinstance(valueOfFeat, dict):
        classLabel = classify(valueOfFeat, featLabels, testVec)
    else:
        classLabel = valueOfFeat
    return classLabel


def storeTree(inputTree, filename):  # 存储树
    import pickle
    fw = open(filename, 'w')
    pickle.dump(inputTree, fw)
    fw.close()


def grabTree(filename):  # 打开树
    import pickle
    fr = open(filename)
    return pickle.load(fr)


def test():
    with open('lenses.txt') as f:
        lenses = [line.strip().split('\t') for line in f.readlines()]
    lesensLabels = ['age', 'prescript', 'astigmatic', 'tearRate']
    myTree = createTree(lenses, lesensLabels)
    # print(myTree)
    # print(lenses[0])

if __name__ == '__main__':
    # dataSet, labels = createDataSet()
    # shannonEnt = calcShannonEnt(dataSet)
    # retDataSet = splitDataSet(dataSet, 0, 0)
    # myTree = createTree(dataSet,labels)
    # classLabel = classify(myTree, labels, [1,1])
    # print(classLabel)
    test()