Machine_Learning_in_Action03 - Decision_trees

Decision Trees

decision tree algorithm

测量数据一致性

使用递归构建决策树

使用 matplotlib 展示决策树

Decision Trees

决策树相对knn的优势是对数据有一定的洞见，能帮助人们理解数据
决策树常用于专家系统
用决策树得到的规则常与人类专家的经验比较
实现 ID3 算法

决策树

优点：
- 计算量少
- 便于人们理解
- 允许有缺失值
- 可以处理无关特征
缺点：
- 易过拟合
适用数值类型：
- 数值型
- 名词性数据
相关理论：
- 信息论 - 熵
基本思路：

首先决定在哪个特征上分割数据集，为此，需要尝试每个特征，然后找出最好的结果。
然后将数据集按照上一步选出的特征分割数据集
遍历每个分支，如果该分支的所有数据都分为同一类，则该分支已正确分类，无需继续分割；否则重复上述两个步骤

步骤：

收集数据
准备，需要离散数据，连续性数据需要转换为离散数据
分析，可视化
训练：构建决策树
测试：计算误差
应用

数据

判断五种动物能否不浮出水面而能生存，以及是否有脚蹼

|Can survive without coming to surface? |Has flippers?| Fish?|
| - | - | - | - |
|1| Yes| Yes| Yes|
|2| Yes| Yes| Yes|
|3| Yes| No| No|
|4| No| Yes| No|
|5| No| Yes| No|

def createDataSet():
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing','flippers']
    return dataSet, labels

信息增益

定义

来源于信息论，信息增益为数据集分割前后信息熵之差

信息量：是对信息的量化

\[l(x_i) = log_2{p(x_i)} \]

信息熵：信息量的期望值

\[H = - \sum_{i=1}^{n}{p(x_i)log_2{p(x_i)}} \]

\(i\) 是指第i类

实现

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

按照属性分割数据集

def splitDataSet(dataSet, axis, value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

def splitDataSet_test():
    dataSet, labels = createDataSet()
    ret = splitDataSet(dataSet, 0, 1)
    print(ret)

选择最好的特征

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
        if (infoGain > bestInfoGain):
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature

def chooseBestFeatureToSplit_test():
    dataSet, labels = createDataSet()
    best_feature = chooseBestFeatureToSplit(dataSet)
    print(best_feature)

创建树

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):
    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]
    myTree = {bestFeatLabel:{}}
    del(labels[bestFeat])
    featValues = [example[bestFeat] for example in dataSet]
    uniqueVals = set(featValues)
    for value in uniqueVals:
        subLabels = labels[:]
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
    return myTree

def createTree_test():
    dataSet, labels = createDataSet()
    t = createTree(dataSet, labels)
    print(t)

可视化决策树

def plotNode(nodeTxt, centerPt, parentPt, nodeType, arrow_args):
    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)

def plotTree(myTree, parentPt, nodeTxt, decisionNode, leafNode, arrow_args):
    numLeafs = getNumLeafs(myTree)
    getTreeDepth(myTree)
    firstStr = list(myTree.keys())[0]
    cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)
    plotMidText(cntrPt, parentPt, nodeTxt)
    plotNode(firstStr, cntrPt, parentPt, decisionNode, arrow_args)
    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), decisionNode, leafNode, arrow_args)
        else:
            plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW
            plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode, arrow_args)
            plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key))
    plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalD

def createPlot(inTree, decisionNode, leafNode, arrow_args):
    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), '', decisionNode, leafNode, arrow_args)
    plt.show()

def plot_tree1():
    dataSet, labels = createDataSet()
    t = createTree(dataSet, labels)

    decisionNode = dict(boxstyle="sawtooth", fc="0.8")
    leafNode = dict(boxstyle="round4", fc="0.8")
    arrow_args = dict(arrowstyle="<-")

    createPlot(t, decisionNode, leafNode, arrow_args)

结果

使用决策树分类

def classify(inputTree,featLabels,testVec):
    firstStr = list(inputTree.keys())[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)
    for key in secondDict.keys():
        if testVec[featIndex] == key:
            if type(secondDict[key]).__name__=='dict':
                classLabel = classify(secondDict[key],featLabels,testVec)
            else: classLabel = secondDict[key]
    return classLabel

def classify_test():
    dataSet, labels = createDataSet()
    t = createTree(dataSet, labels.copy())
    print(dataSet, labels)
    print(t)

    label = classify(t, labels, [1,0])
    print(label)

完整代码

import os
import operator
import math
import numpy as np
import matplotlib.pyplot as plt


def createDataSet():
    dataSet = [[1, 1, 'yes'],
               [1, 1, 'yes'],
               [1, 0, 'no'],
               [0, 1, 'no'],
               [0, 1, 'no']]
    labels = ['no surfacing','flippers']
    return dataSet, 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 * math.log(prob,2)
    return shannonEnt

def entropy_test():
    dataSet, labels = createDataSet()
    ent = calcShannonEnt(dataSet)
    print(ent)


def splitDataSet(dataSet, axis, value):
    retDataSet = []
    for featVec in dataSet:
        if featVec[axis] == value:
            reducedFeatVec = featVec[:axis]
            reducedFeatVec.extend(featVec[axis+1:])
            retDataSet.append(reducedFeatVec)
    return retDataSet

def splitDataSet_test():
    dataSet, labels = createDataSet()
    ret = splitDataSet(dataSet, 0, 1)
    print(ret)


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
        if (infoGain > bestInfoGain):
            bestInfoGain = infoGain
            bestFeature = i
    return bestFeature

def chooseBestFeatureToSplit_test():
    dataSet, labels = createDataSet()
    best_feature = chooseBestFeatureToSplit(dataSet)
    print(best_feature)


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 majorityCnt_test():
    dataSet, labels = createDataSet()
    labels_sort = majorityCnt(labels)
    print(labels_sort)


def createTree(dataSet,labels):
    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]
    myTree = {bestFeatLabel:{}}
    del(labels[bestFeat])
    featValues = [example[bestFeat] for example in dataSet]
    uniqueVals = set(featValues)
    for value in uniqueVals:
        subLabels = labels[:]
        myTree[bestFeatLabel][value] = createTree(splitDataSet(dataSet, bestFeat, value),subLabels)
    return myTree

def createTree_test():
    dataSet, labels = createDataSet()
    t = createTree(dataSet, labels)
    print(t)


# plotting0
def plotNode(nodeTxt, centerPt, parentPt, nodeType, arrow_args):
    createPlot.ax1.annotate(nodeTxt, xy=parentPt, xycoords='axes fraction', xytext=centerPt, textcoords='axes fraction', va="center", ha="center", bbox=nodeType, arrowprops=arrow_args)

def createPlot(decisionNode, leafNode, arrow_args):
    fig = plt.figure(1, facecolor='white')
    fig.clf()
    createPlot.ax1 = plt.subplot(111, frameon=False)
    plotNode('a decision node', (0.5, 0.1), (0.1, 0.5), decisionNode, arrow_args)
    plotNode('a leaf node', (0.8, 0.1), (0.3, 0.8), leafNode, arrow_args)
    plt.show()

def plot_tree0():
    decisionNode = dict(boxstyle="sawtooth", fc="0.8")
    leafNode = dict(boxstyle="round4", fc="0.8")
    arrow_args = dict(arrowstyle="<-")

    createPlot(decisionNode, leafNode, arrow_args)


# construct tree
def getNumLeafs(myTree):
    numLeafs = 0
    firstStr = list(myTree.keys())[0]
    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):
    maxDepth = 0
    firstStr = list(myTree.keys())[0]
    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 tree_test():
    dataSet, labels = createDataSet()
    t = createTree(dataSet, labels)

    numLeafs = getNumLeafs(t)
    depth = getTreeDepth(t)

    print(t)
    print(numLeafs, depth)


# plotting1
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)

def plotTree(myTree, parentPt, nodeTxt, decisionNode, leafNode, arrow_args):
    numLeafs = getNumLeafs(myTree)
    getTreeDepth(myTree)
    firstStr = list(myTree.keys())[0]
    cntrPt = (plotTree.xOff + (1.0 + float(numLeafs))/2.0/plotTree.totalW, plotTree.yOff)
    plotMidText(cntrPt, parentPt, nodeTxt)
    plotNode(firstStr, cntrPt, parentPt, decisionNode, arrow_args)
    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), decisionNode, leafNode, arrow_args)
        else:
            plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW
            plotNode(secondDict[key], (plotTree.xOff, plotTree.yOff), cntrPt, leafNode, arrow_args)
            plotMidText((plotTree.xOff, plotTree.yOff), cntrPt, str(key))
    plotTree.yOff = plotTree.yOff + 1.0/plotTree.totalD

def createPlot(inTree, decisionNode, leafNode, arrow_args):
    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), '', decisionNode, leafNode, arrow_args)
    plt.show()

def plot_tree1():
    dataSet, labels = createDataSet()
    t = createTree(dataSet, labels)

    decisionNode = dict(boxstyle="sawtooth", fc="0.8")
    leafNode = dict(boxstyle="round4", fc="0.8")
    arrow_args = dict(arrowstyle="<-")

    createPlot(t, decisionNode, leafNode, arrow_args)


def classify(inputTree,featLabels,testVec):
    firstStr = list(inputTree.keys())[0]
    secondDict = inputTree[firstStr]
    featIndex = featLabels.index(firstStr)
    for key in secondDict.keys():
        if testVec[featIndex] == key:
            if type(secondDict[key]).__name__=='dict':
                classLabel = classify(secondDict[key],featLabels,testVec)
            else: classLabel = secondDict[key]
    return classLabel

def classify_test():
    dataSet, labels = createDataSet()
    t = createTree(dataSet, labels.copy())
    print(dataSet, labels)
    print(t)

    label = classify(t, labels, [1,0])
    print(label)

if __name__ == '__main__':
    # entropy_test()
    # splitDataSet_test()
    # chooseBestFeatureToSplit_test()
    # majorityCnt_test()
    # createTree_test()
    # plot_tree0()
    # tree_test()

    # plot_tree1()

    classify_test()

posted @ 2019-07-27 20:17 keep-minding 阅读(173) 评论(0) 收藏举报

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