回归树-----生成回归树
当数据拥有众多属性并且属性间关系复杂时，前面所讲的回归算法就显得太难了。今天我们就讨论一种树型的回归算法。前面讲过一个树，叫做决策树，构建决策树时需要利用信息增益来计算出最佳的分类特征然后不断的从剩余的特征中找出最佳的分类特征进行分类，这种方法叫做ID3.今天我们构建树所用的切分数据的方法有所不同，用的是二分法。其主体思想也是找到最佳的分类特征：ex00.txt （提取码：b416）
from numpy import *
def loadDataSet(fileName):
dataMat = []
fr = open(fileName)
for line in fr.readlines():
curLine = line.strip().split('\t')
fltLine = map(float,curLine)
dataMat.append(fltLine)
return dataMat
def binSplitDataSet(dataSet, feature, value):
mat0 = dataSet[nonzero(dataSet[:,feature] > value)[0],:][0]
mat1 = dataSet[nonzero(dataSet[:,feature] <= value)[0],:][0]
return mat0,mat1
def createTree(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):
feat, val = chooseBestSplit(dataSet, leafType, errType, ops)
if feat == None: return val
retTree = {}
retTree['spInd'] = feat
retTree['spVal'] = val
lSet, rSet = binSplitDataSet(dataSet, feat, val)
retTree['left'] = createTree(lSet, leafType, errType, ops)
retTree['right'] = createTree(rSet, leafType, errType, ops)
return retTree
上面代码的第一个函数依旧是文件读写。第二个函数有三个输入参数，数据集合，待切分的特征和该特征的值，通过给定的特征以及特征值将数据集合切分到两个子集中，第三
个函数用于建树，在这个函数有四个输入参数，数据集、建立叶子节点函数、误差计算函数和一个构建树所需的元组参数首先会用到切分函数对数据集进行切分然后判断是否满足停止条件接下来递归调用函数来构建树。下面我们着重讲解数据切分：
def regLeaf(dataSet):
return mean(dataSet[:,-1])
def regErr(dataSet):
return var(dataSet[:,-1]) * shape(dataSet)[0]
def chooseBestSplit(dataSet, leafType=regLeaf, errType=regErr, ops=(1,4)):
tolS = ops[0]; tolN = ops[1]
if len(set(dataSet[:,-1].T.tolist()[0])) == 1:
return None, leafType(dataSet)
m,n = shape(dataSet)
S = errType(dataSet)
bestS = inf; bestIndex = 0; bestValue = 0
for featIndex in range(n-1):
for splitVal in set(dataSet[:,featIndex]):
mat0, mat1 = binSplitDataSet(dataSet, featIndex, splitVal)
if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN): continue
newS = errType(mat0) + errType(mat1)
if newS < bestS:
bestIndex = featIndex
bestValue = splitVal
bestS = newS
if (S - bestS) < tolS:
return None, leafType(dataSet)
mat0, mat1 = binSplitDataSet(dataSet, bestIndex, bestValue)
if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):
return None, leafType(dataSet)
return bestIndex,bestValue