統計學習方法 習題5.2 python實現

根據表5.2所示的數據，用平方誤差損失準則生成二叉迴歸樹

二叉迴歸樹的算法爲：

其中公式5.21中的c1,c2分別爲R1和R2上數據的平均值

代碼仿照機器學習實戰上關於決策樹實現（遞歸的建立一棵樹）保存爲cart.py：

#coding:utf-8
import numpy as np

#數據集
def createDataSet():
    dataSet = [4.5,4.75,4.91,5.34,5.8,7.05,7.9,8.23,8.7,9]
    datalabel = [1,2,3,4,5,6,7,8,9,10]
    return dataSet,datalabel

#計算數據集的平方誤差
def calcMSE(dataSet):
    means = np.mean(dataSet)
    sums = sum([(i-means)*(i-means) for i in dataSet])*1.0
    return sums

#選擇最優的劃分點
def chooseBestFeatureToSplit(dataSet):
    nums = len(dataSet)-1
    if nums == 0:
        return 0
    best = 0
    bestMES = 100000
    for i in range(nums):
        temp = calcMSE(dataSet[:i+1]) + calcMSE(dataSet[i+1:])
        if temp <= bestMES:
            bestMES = temp
            best = i
    return best

# def getkeyofromvalue(dataSet,value):
#     u = -1
#     for i in range(len(dataSet)):
#         if dataSet[i] == value:
#             u = i
#     return u

#建樹過程
def createTree(dataSet,datalabel,left,right):
    if right-left == 1:
        #return dataSet[left]
        return datalabel[left]
    if left >= right:
        return -1
    #最優劃分函數加上left爲原數據集上的最優劃分下標
    bestchoose = left + chooseBestFeatureToSplit(dataSet[left:right])
    #print bestchoose+1
    mytree = {datalabel[bestchoose]:{}}
    mytree[datalabel[bestchoose]]['left'] = createTree(dataSet,datalabel,left,bestchoose)
    mytree[datalabel[bestchoose]]['right'] = createTree(dataSet,datalabel,bestchoose+1,right)
    return mytree

調用方法：

import cart
mydat,myla = cart.createDataSet()
myt = cart.createTree(mydat,myla,0,len(mydat))
print myt

結果（沒有進行可視化操作）：