mirror of
https://github.com/apachecn/ailearning.git
synced 2026-02-11 14:26:04 +08:00
344 lines
12 KiB
Python
344 lines
12 KiB
Python
#!/usr/bin/python
|
||
# coding:utf8
|
||
'''
|
||
Created on Feb 4, 2011
|
||
Update on 2017-05-18
|
||
Tree-Based Regression Methods Source Code for Machine Learning in Action Ch. 9
|
||
@author: Peter Harrington/片刻
|
||
《机器学习实战》更新地址：https://github.com/apachecn/MachineLearning
|
||
'''
|
||
print(__doc__)
|
||
from numpy import *
|
||
|
||
|
||
# 默认解析的数据是用tab分隔，并且是数值类型
|
||
# general function to parse tab -delimited floats
|
||
def loadDataSet(fileName):
|
||
"""loadDataSet(解析每一行，并转化为float类型)
|
||
|
||
Args:
|
||
fileName 文件名
|
||
Returns:
|
||
dataMat 每一行的数据集array类型
|
||
Raises:
|
||
"""
|
||
# 假定最后一列是结果值
|
||
# assume last column is target value
|
||
dataMat = []
|
||
fr = open(fileName)
|
||
for line in fr.readlines():
|
||
curLine = line.strip().split('\t')
|
||
# 将所有的元素转化为float类型
|
||
# map all elements to float()
|
||
fltLine = map(float, curLine)
|
||
dataMat.append(fltLine)
|
||
return dataMat
|
||
|
||
|
||
def binSplitDataSet(dataSet, feature, value):
|
||
"""binSplitDataSet(将数据集，按照feature列的value进行 二元切分)
|
||
|
||
Args:
|
||
dataMat 数据集
|
||
feature 特征列
|
||
value 特征列要比较的值
|
||
Returns:
|
||
mat0 小于的数据集在左边
|
||
mat1 大于的数据集在右边
|
||
Raises:
|
||
"""
|
||
# # 测试案例
|
||
# print 'dataSet[:, feature]=', dataSet[:, feature]
|
||
# print 'nonzero(dataSet[:, feature] > value)[0]=', nonzero(dataSet[:, feature] > value)[0]
|
||
# print 'nonzero(dataSet[:, feature] <= value)[0]=', nonzero(dataSet[:, feature] <= value)[0]
|
||
|
||
# dataSet[:, feature] 取去每一行中，第1列的值(从0开始算)
|
||
# nonzero(dataSet[:, feature] > value) 返回结果为true行的index下标
|
||
mat0 = dataSet[nonzero(dataSet[:, feature] <= value)[0], :]
|
||
mat1 = dataSet[nonzero(dataSet[:, feature] > value)[0], :]
|
||
return mat0, mat1
|
||
|
||
|
||
# 返回每一个叶子结点的均值
|
||
# returns the value used for each leaf
|
||
def regLeaf(dataSet):
|
||
return mean(dataSet[:, -1])
|
||
|
||
|
||
# 计算总方差=方差*样本数
|
||
def regErr(dataSet):
|
||
# shape(dataSet)[0] 表示行数
|
||
return var(dataSet[:, -1]) * shape(dataSet)[0]
|
||
|
||
|
||
# 1.用最佳方式切分数据集
|
||
# 2.生成相应的叶节点
|
||
def chooseBestSplit(dataSet, leafType=regLeaf, errType=regErr, ops=(1, 4)):
|
||
"""chooseBestSplit(用最佳方式切分数据集 和 生成相应的叶节点)
|
||
|
||
Args:
|
||
dataSet 加载的原始数据集
|
||
leafType 建立叶子点的函数
|
||
errType 误差计算函数(求总方差)
|
||
ops [容许误差下降值，切分的最少样本数]
|
||
Returns:
|
||
bestIndex feature的index坐标
|
||
bestValue 切分的最优值
|
||
Raises:
|
||
"""
|
||
tolS = ops[0]
|
||
tolN = ops[1]
|
||
# 如果结果集(最后一列为1个变量)，就返回推出
|
||
# .T 对数据集进行转置
|
||
# .tolist()[0] 转化为数组并取第0列
|
||
if len(set(dataSet[:, -1].T.tolist()[0])) == 1:
|
||
# exit cond 1
|
||
return None, leafType(dataSet)
|
||
# 计算行列值
|
||
m, n = shape(dataSet)
|
||
# 无分类误差的总方差和
|
||
# the choice of the best feature is driven by Reduction in RSS error from mean
|
||
S = errType(dataSet)
|
||
# inf 正无穷大
|
||
bestS, bestIndex, bestValue = inf, 0, 0
|
||
# 循环处理每一列对应的feature值
|
||
for featIndex in range(n-1):
|
||
# [0]表示这一列的[所有行]，不要[0]就是一个array[[所有行]]
|
||
for splitVal in set(dataSet[:, featIndex].T.tolist()[0]):
|
||
# 对该列进行分组，然后组内的成员的val值进行 二元切分
|
||
mat0, mat1 = binSplitDataSet(dataSet, featIndex, splitVal)
|
||
# 判断二元切分的方式的元素数量是否符合预期
|
||
if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):
|
||
continue
|
||
newS = errType(mat0) + errType(mat1)
|
||
# 如果二元切分，算出来的误差在可接受范围内，那么就记录切分点，并记录最小误差
|
||
if newS < bestS:
|
||
bestIndex = featIndex
|
||
bestValue = splitVal
|
||
bestS = newS
|
||
# 判断二元切分的方式的元素误差是否符合预期
|
||
# if the decrease (S-bestS) is less than a threshold don't do the split
|
||
if (S - bestS) < tolS:
|
||
return None, leafType(dataSet)
|
||
mat0, mat1 = binSplitDataSet(dataSet, bestIndex, bestValue)
|
||
# 对整体的成员进行判断，是否符合预期
|
||
if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):
|
||
return None, leafType(dataSet)
|
||
return bestIndex, bestValue
|
||
|
||
|
||
# assume dataSet is NumPy Mat so we can array filtering
|
||
def createTree(dataSet, leafType=regLeaf, errType=regErr, ops=(1, 4)):
|
||
"""createTree(获取回归树)
|
||
|
||
Args:
|
||
dataSet 加载的原始数据集
|
||
leafType 建立叶子点的函数
|
||
errType 误差计算函数
|
||
ops=(1, 4) [容许误差下降值，切分的最少样本数]
|
||
Returns:
|
||
retTree 决策树最后的结果
|
||
"""
|
||
# 选择最好的切分方式： feature索引值，最优切分值
|
||
# choose the best split
|
||
feat, val = chooseBestSplit(dataSet, leafType, errType, ops)
|
||
# if the splitting hit a stop condition return val
|
||
if feat is None:
|
||
return val
|
||
retTree = {}
|
||
retTree['spInd'] = feat
|
||
retTree['spVal'] = val
|
||
# 大于在右边，小于在左边，分为2个数据集
|
||
lSet, rSet = binSplitDataSet(dataSet, feat, val)
|
||
# 递归的进行调用
|
||
retTree['left'] = createTree(lSet, leafType, errType, ops)
|
||
retTree['right'] = createTree(rSet, leafType, errType, ops)
|
||
return retTree
|
||
|
||
|
||
# 判断节点是否是一个字典
|
||
def isTree(obj):
|
||
return (type(obj).__name__ == 'dict')
|
||
|
||
|
||
# 计算左右枝丫的均值
|
||
def getMean(tree):
|
||
if isTree(tree['right']):
|
||
tree['right'] = getMean(tree['right'])
|
||
if isTree(tree['left']):
|
||
tree['left'] = getMean(tree['left'])
|
||
return (tree['left']+tree['right'])/2.0
|
||
|
||
|
||
# 检查是否适合合并分枝
|
||
def prune(tree, testData):
|
||
# 判断是否测试数据集没有数据，如果没有，就直接返回tree本身的均值
|
||
if shape(testData)[0] == 0:
|
||
return getMean(tree)
|
||
|
||
# 判断分枝是否是dict字典，如果是就将测试数据集进行切分
|
||
if (isTree(tree['right']) or isTree(tree['left'])):
|
||
lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
|
||
# 如果是左边分枝是字典，就传入左边的数据集和左边的分枝，进行递归
|
||
if isTree(tree['left']):
|
||
tree['left'] = prune(tree['left'], lSet)
|
||
# 如果是右边分枝是字典，就传入左边的数据集和左边的分枝，进行递归
|
||
if isTree(tree['right']):
|
||
tree['right'] = prune(tree['right'], rSet)
|
||
|
||
# 如果左右两边同时都不是dict字典，那么分割测试数据集。
|
||
# 1. 如果正确
|
||
# * 那么计算一下总方差 和 该结果集的本身不分枝的总方差比较
|
||
# * 如果 合并的总方差 < 不合并的总方差，那么就进行合并
|
||
# 注意返回的结果： 如果可以合并，原来的dict就变为了 数值
|
||
if not isTree(tree['left']) and not isTree(tree['right']):
|
||
lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
|
||
# power(x, y)表示x的y次方
|
||
errorNoMerge = sum(power(lSet[:, -1] - tree['left'], 2)) + sum(power(rSet[:, -1] - tree['right'], 2))
|
||
treeMean = (tree['left'] + tree['right'])/2.0
|
||
errorMerge = sum(power(testData[:, -1] - treeMean, 2))
|
||
# 如果 合并的总方差 < 不合并的总方差，那么就进行合并
|
||
if errorMerge < errorNoMerge:
|
||
print "merging"
|
||
return treeMean
|
||
else:
|
||
return tree
|
||
else:
|
||
return tree
|
||
|
||
|
||
# 得到模型的ws系数：f(x) = x0 + x1*featrue1+ x3*featrue2 ...
|
||
# create linear model and return coeficients
|
||
def modelLeaf(dataSet):
|
||
ws, X, Y = linearSolve(dataSet)
|
||
return ws
|
||
|
||
|
||
# 计算线性模型的误差值
|
||
def modelErr(dataSet):
|
||
ws, X, Y = linearSolve(dataSet)
|
||
yHat = X * ws
|
||
# print corrcoef(yHat, Y, rowvar=0)
|
||
return sum(power(Y - yHat, 2))
|
||
|
||
|
||
# helper function used in two places
|
||
def linearSolve(dataSet):
|
||
m, n = shape(dataSet)
|
||
# 产生一个关于1的矩阵
|
||
X = mat(ones((m, n)))
|
||
Y = mat(ones((m, 1)))
|
||
# X的0列为1，常数项，用于计算平衡误差
|
||
X[:, 1: n] = dataSet[:, 0: n-1]
|
||
Y = dataSet[:, -1]
|
||
|
||
# 转置矩阵*矩阵
|
||
xTx = X.T * X
|
||
# 如果矩阵的逆不存在，会造成程序异常
|
||
if linalg.det(xTx) == 0.0:
|
||
raise NameError('This matrix is singular, cannot do inverse,\ntry increasing the second value of ops')
|
||
# 最小二乘法求最优解: w0*1+w1*x1=y
|
||
ws = xTx.I * (X.T * Y)
|
||
return ws, X, Y
|
||
|
||
|
||
# 回归树测试案例
|
||
def regTreeEval(model, inDat):
|
||
return float(model)
|
||
|
||
|
||
# 模型树测试案例
|
||
def modelTreeEval(model, inDat):
|
||
n = shape(inDat)[1]
|
||
X = mat(ones((1, n+1)))
|
||
X[:, 1: n+1] = inDat
|
||
# print X, model
|
||
return float(X * model)
|
||
|
||
|
||
# 计算预测的结果
|
||
def treeForeCast(tree, inData, modelEval=regTreeEval):
|
||
if not isTree(tree):
|
||
return modelEval(tree, inData)
|
||
if inData[tree['spInd']] <= tree['spVal']:
|
||
if isTree(tree['left']):
|
||
return treeForeCast(tree['left'], inData, modelEval)
|
||
else:
|
||
return modelEval(tree['left'], inData)
|
||
else:
|
||
if isTree(tree['right']):
|
||
return treeForeCast(tree['right'], inData, modelEval)
|
||
else:
|
||
return modelEval(tree['right'], inData)
|
||
|
||
|
||
# 预测结果
|
||
def createForeCast(tree, testData, modelEval=regTreeEval):
|
||
m = len(testData)
|
||
yHat = mat(zeros((m, 1)))
|
||
for i in range(m):
|
||
yHat[i, 0] = treeForeCast(tree, mat(testData[i]), modelEval)
|
||
return yHat
|
||
|
||
|
||
if __name__ == "__main__":
|
||
# # 测试数据集
|
||
# testMat = mat(eye(4))
|
||
# print testMat
|
||
# print type(testMat)
|
||
# mat0, mat1 = binSplitDataSet(testMat, 1, 0.5)
|
||
# print mat0, '\n-----------\n', mat1
|
||
|
||
# # 回归树
|
||
# myDat = loadDataSet('input/9.RegTrees/data1.txt')
|
||
# # myDat = loadDataSet('input/9.RegTrees/data2.txt')
|
||
# # print 'myDat=', myDat
|
||
# myMat = mat(myDat)
|
||
# # print 'myMat=', myMat
|
||
# myTree = createTree(myMat)
|
||
# print myTree
|
||
|
||
# # 1. 预剪枝就是：提起设置最大误差数和最少元素数
|
||
# myDat = loadDataSet('input/9.RegTrees/data3.txt')
|
||
# myMat = mat(myDat)
|
||
# myTree = createTree(myMat, ops=(0, 1))
|
||
# print myTree
|
||
|
||
# # 2. 后剪枝就是：通过测试数据，对预测模型进行合并判断
|
||
# myDatTest = loadDataSet('input/9.RegTrees/data3test.txt')
|
||
# myMat2Test = mat(myDatTest)
|
||
# myFinalTree = prune(myTree, myMat2Test)
|
||
# print '\n\n\n-------------------'
|
||
# print myFinalTree
|
||
|
||
# # --------
|
||
# # 模型树求解
|
||
# myDat = loadDataSet('input/9.RegTrees/data4.txt')
|
||
# myMat = mat(myDat)
|
||
# myTree = createTree(myMat, modelLeaf, modelErr)
|
||
# print myTree
|
||
|
||
# 回归树 VS 模型树 VS 线性回归
|
||
trainMat = mat(loadDataSet('input/9.RegTrees/bikeSpeedVsIq_train.txt'))
|
||
testMat = mat(loadDataSet('input/9.RegTrees/bikeSpeedVsIq_test.txt'))
|
||
# 回归树
|
||
myTree1 = createTree(trainMat, ops=(1, 20))
|
||
print myTree1
|
||
yHat1 = createForeCast(myTree1, testMat[:, 0])
|
||
print "回归树:", corrcoef(yHat1, testMat[:, 1],rowvar=0)[0, 1]
|
||
|
||
# 模型树
|
||
myTree2 = createTree(trainMat, modelLeaf, modelErr, ops=(1, 20))
|
||
yHat2 = createForeCast(myTree2, testMat[:, 0], modelTreeEval)
|
||
print myTree2
|
||
print "模型树:", corrcoef(yHat2, testMat[:, 1],rowvar=0)[0, 1]
|
||
|
||
# 线性回归
|
||
ws, X, Y = linearSolve(trainMat)
|
||
print ws
|
||
m = len(testMat[:, 0])
|
||
yHat3 = mat(zeros((m, 1)))
|
||
for i in range(shape(testMat)[0]):
|
||
yHat3[i] = testMat[i, 0]*ws[1, 0] + ws[0, 0]
|
||
print "线性回归:", corrcoef(yHat3, testMat[:, 1],rowvar=0)[0, 1]
|