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356 lines
14 KiB
Python
356 lines
14 KiB
Python
#!/usr/bin/python
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# coding:utf8
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'''
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Created on Feb 4, 2011
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Update on 2017-05-18
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Tree-Based Regression Methods Source Code for Machine Learning in Action Ch. 9
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@author: Peter Harrington/片刻/小瑶
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《机器学习实战》更新地址：https://github.com/apachecn/MachineLearning
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'''
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print(__doc__)
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from numpy import *
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# 默认解析的数据是用tab分隔，并且是数值类型
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# general function to parse tab -delimited floats
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def loadDataSet(fileName):
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"""loadDataSet(解析每一行，并转化为float类型)
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Desc：该函数读取一个以 tab 键为分隔符的文件，然后将每行的内容保存成一组浮点数
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Args:
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fileName 文件名
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Returns:
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dataMat 每一行的数据集array类型
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Raises:
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"""
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# 假定最后一列是结果值
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# assume last column is target value
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dataMat = []
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fr = open(fileName)
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for line in fr.readlines():
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curLine = line.strip().split('\t')
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# 将所有的元素转化为float类型
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# map all elements to float()
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# map() 函数具体的含义，可见 https://my.oschina.net/zyzzy/blog/115096
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fltLine = map(float, curLine)
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dataMat.append(fltLine)
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return dataMat
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def binSplitDataSet(dataSet, feature, value):
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"""binSplitDataSet(将数据集，按照feature列的value进行 二元切分)
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Description：在给定特征和特征值的情况下，该函数通过数组过滤方式将上述数据集合切分得到两个子集并返回。
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Args:
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dataMat 数据集
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feature 待切分的特征列
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value 特征列要比较的值
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Returns:
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mat0 小于等于 value 的数据集在左边
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mat1 大于 value 的数据集在右边
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Raises:
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"""
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# # 测试案例
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# print 'dataSet[:, feature]=', dataSet[:, feature]
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# print 'nonzero(dataSet[:, feature] > value)[0]=', nonzero(dataSet[:, feature] > value)[0]
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# print 'nonzero(dataSet[:, feature] <= value)[0]=', nonzero(dataSet[:, feature] <= value)[0]
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# dataSet[:, feature] 取去每一行中，第1列的值(从0开始算)
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# nonzero(dataSet[:, feature] > value) 返回结果为true行的index下标
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mat0 = dataSet[nonzero(dataSet[:, feature] <= value)[0], :]
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mat1 = dataSet[nonzero(dataSet[:, feature] > value)[0], :]
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return mat0, mat1
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# 返回每一个叶子结点的均值
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# returns the value used for each leaf
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# 我的理解是：regLeaf 是产生叶节点的函数，就是求均值，即用聚类中心点来代表这类数据
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def regLeaf(dataSet):
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return mean(dataSet[:, -1])
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# 计算总方差=方差*样本数
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# 我的理解是：求这组数据的方差，即通过决策树划分，可以让靠近的数据分到同一类中去
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def regErr(dataSet):
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# shape(dataSet)[0] 表示行数
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return var(dataSet[:, -1]) * shape(dataSet)[0]
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# 1.用最佳方式切分数据集
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# 2.生成相应的叶节点
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def chooseBestSplit(dataSet, leafType=regLeaf, errType=regErr, ops=(1, 4)):
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"""chooseBestSplit(用最佳方式切分数据集 和 生成相应的叶节点)
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Args:
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dataSet 加载的原始数据集
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leafType 建立叶子点的函数
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errType 误差计算函数(求总方差)
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ops [容许误差下降值，切分的最少样本数]。
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Returns:
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bestIndex feature的index坐标
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bestValue 切分的最优值
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Raises:
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"""
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# ops=(1,4)，非常重要，因为它决定了决策树划分停止的threshold值，被称为预剪枝（prepruning），其实也就是用于控制函数的停止时机。
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# 之所以这样说，是因为它防止决策树的过拟合，所以当误差的下降值小于tolS，或划分后的集合size小于tolN时，选择停止继续划分。
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# 最小误差下降值，划分后的误差减小小于这个差值，就不用继续划分
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tolS = ops[0]
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# 划分最小 size 小于，就不继续划分了
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tolN = ops[1]
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# 如果结果集(最后一列为1个变量)，就返回退出
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# .T 对数据集进行转置
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# .tolist()[0] 转化为数组并取第0列
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if len(set(dataSet[:, -1].T.tolist()[0])) == 1: # 如果集合size为1，不用继续划分。
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# exit cond 1
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return None, leafType(dataSet)
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# 计算行列值
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m, n = shape(dataSet)
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# 无分类误差的总方差和
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# the choice of the best feature is driven by Reduction in RSS error from mean
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S = errType(dataSet)
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# inf 正无穷大
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bestS, bestIndex, bestValue = inf, 0, 0
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# 循环处理每一列对应的feature值
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for featIndex in range(n-1): # 对于每个特征
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# [0]表示这一列的[所有行]，不要[0]就是一个array[[所有行]]
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for splitVal in set(dataSet[:, featIndex].T.tolist()[0]):
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# 对该列进行分组，然后组内的成员的val值进行 二元切分
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mat0, mat1 = binSplitDataSet(dataSet, featIndex, splitVal)
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# 判断二元切分的方式的元素数量是否符合预期
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if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN):
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continue
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newS = errType(mat0) + errType(mat1)
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# 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
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# 如果划分后误差小于 bestS，则说明找到了新的bestS
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if newS < bestS:
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bestIndex = featIndex
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bestValue = splitVal
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bestS = newS
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# 判断二元切分的方式的元素误差是否符合预期
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# if the decrease (S-bestS) is less than a threshold don't do the split
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if (S - bestS) < tolS:
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return None, leafType(dataSet)
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mat0, mat1 = binSplitDataSet(dataSet, bestIndex, bestValue)
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# 对整体的成员进行判断，是否符合预期
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# 如果集合的 size 小于 tolN
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if (shape(mat0)[0] < tolN) or (shape(mat1)[0] < tolN): # 当最佳划分后，集合过小，也不划分，产生叶节点
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return None, leafType(dataSet)
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return bestIndex, bestValue
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# assume dataSet is NumPy Mat so we can array filtering
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# 假设 dataSet 是 NumPy Mat 类型的，那么我们可以进行 array 过滤
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def createTree(dataSet, leafType=regLeaf, errType=regErr, ops=(1, 4)):
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"""createTree(获取回归树)
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Description：递归函数：如果构建的是回归树，该模型是一个常数，如果是模型树，其模型师一个线性方程。
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Args:
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dataSet 加载的原始数据集
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leafType 建立叶子点的函数
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errType 误差计算函数
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ops=(1, 4) [容许误差下降值，切分的最少样本数]
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Returns:
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retTree 决策树最后的结果
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"""
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# 选择最好的切分方式： feature索引值，最优切分值
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# choose the best split
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feat, val = chooseBestSplit(dataSet, leafType, errType, ops)
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# if the splitting hit a stop condition return val
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# 如果 splitting 达到一个停止条件，那么返回 val
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if feat is None:
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return val
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retTree = {}
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retTree['spInd'] = feat
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retTree['spVal'] = val
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# 大于在右边，小于在左边，分为2个数据集
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lSet, rSet = binSplitDataSet(dataSet, feat, val)
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# 递归的进行调用，在左右子树中继续递归生成树
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retTree['left'] = createTree(lSet, leafType, errType, ops)
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retTree['right'] = createTree(rSet, leafType, errType, ops)
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return retTree
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# 判断节点是否是一个字典
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def isTree(obj):
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return (type(obj).__name__ == 'dict')
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# 计算左右枝丫的均值
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def getMean(tree):
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if isTree(tree['right']):
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tree['right'] = getMean(tree['right'])
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if isTree(tree['left']):
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tree['left'] = getMean(tree['left'])
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return (tree['left']+tree['right'])/2.0
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# 检查是否适合合并分枝
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def prune(tree, testData):
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# 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
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if shape(testData)[0] == 0:
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return getMean(tree)
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# 判断分枝是否是dict字典，如果是就将测试数据集进行切分
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if (isTree(tree['right']) or isTree(tree['left'])):
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lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
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# 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
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if isTree(tree['left']):
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tree['left'] = prune(tree['left'], lSet)
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# 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
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if isTree(tree['right']):
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tree['right'] = prune(tree['right'], rSet)
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# 如果左右两边同时都不是dict字典，那么分割测试数据集。
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# 1. 如果正确
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# * 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
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# * 如果 合并的总方差 < 不合并的总方差，那么就进行合并
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# 注意返回的结果： 如果可以合并，原来的dict就变为了 数值
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if not isTree(tree['left']) and not isTree(tree['right']):
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lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
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# power(x, y)表示x的y次方
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errorNoMerge = sum(power(lSet[:, -1] - tree['left'], 2)) + sum(power(rSet[:, -1] - tree['right'], 2))
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treeMean = (tree['left'] + tree['right'])/2.0
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errorMerge = sum(power(testData[:, -1] - treeMean, 2))
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# 如果 合并的总方差 < 不合并的总方差，那么就进行合并
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if errorMerge < errorNoMerge:
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print "merging"
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return treeMean
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else:
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return tree
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else:
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return tree
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# 得到模型的ws系数：f(x) = x0 + x1*featrue1+ x3*featrue2 ...
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# create linear model and return coeficients
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def modelLeaf(dataSet):
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ws, X, Y = linearSolve(dataSet)
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return ws
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# 计算线性模型的误差值
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def modelErr(dataSet):
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ws, X, Y = linearSolve(dataSet)
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yHat = X * ws
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# print corrcoef(yHat, Y, rowvar=0)
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return sum(power(Y - yHat, 2))
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# helper function used in two places
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def linearSolve(dataSet):
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m, n = shape(dataSet)
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# 产生一个关于1的矩阵
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X = mat(ones((m, n)))
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Y = mat(ones((m, 1)))
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# X的0列为1，常数项，用于计算平衡误差
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X[:, 1: n] = dataSet[:, 0: n-1]
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Y = dataSet[:, -1]
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# 转置矩阵*矩阵
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xTx = X.T * X
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# 如果矩阵的逆不存在，会造成程序异常
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if linalg.det(xTx) == 0.0:
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raise NameError('This matrix is singular, cannot do inverse,\ntry increasing the second value of ops')
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# 最小二乘法求最优解: w0*1+w1*x1=y
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ws = xTx.I * (X.T * Y)
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return ws, X, Y
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# 回归树测试案例
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def regTreeEval(model, inDat):
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return float(model)
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# 模型树测试案例
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def modelTreeEval(model, inDat):
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n = shape(inDat)[1]
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X = mat(ones((1, n+1)))
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X[:, 1: n+1] = inDat
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# print X, model
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return float(X * model)
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# 计算预测的结果
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def treeForeCast(tree, inData, modelEval=regTreeEval):
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if not isTree(tree):
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return modelEval(tree, inData)
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if inData[tree['spInd']] <= tree['spVal']:
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if isTree(tree['left']):
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return treeForeCast(tree['left'], inData, modelEval)
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else:
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return modelEval(tree['left'], inData)
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else:
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if isTree(tree['right']):
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return treeForeCast(tree['right'], inData, modelEval)
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else:
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return modelEval(tree['right'], inData)
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# 预测结果
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def createForeCast(tree, testData, modelEval=regTreeEval):
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m = len(testData)
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yHat = mat(zeros((m, 1)))
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for i in range(m):
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yHat[i, 0] = treeForeCast(tree, mat(testData[i]), modelEval)
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return yHat
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if __name__ == "__main__":
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# # 测试数据集
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# testMat = mat(eye(4))
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# print testMat
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# print type(testMat)
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# mat0, mat1 = binSplitDataSet(testMat, 1, 0.5)
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# print mat0, '\n-----------\n', mat1
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# # 回归树
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# myDat = loadDataSet('input/9.RegTrees/data1.txt')
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# # myDat = loadDataSet('input/9.RegTrees/data2.txt')
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# # print 'myDat=', myDat
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# myMat = mat(myDat)
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# # print 'myMat=', myMat
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# myTree = createTree(myMat)
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# print myTree
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# # 1. 预剪枝就是：提起设置最大误差数和最少元素数
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# myDat = loadDataSet('input/9.RegTrees/data3.txt')
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# myMat = mat(myDat)
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# myTree = createTree(myMat, ops=(0, 1))
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# print myTree
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# # 2. 后剪枝就是：通过测试数据，对预测模型进行合并判断
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# myDatTest = loadDataSet('input/9.RegTrees/data3test.txt')
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# myMat2Test = mat(myDatTest)
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# myFinalTree = prune(myTree, myMat2Test)
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# print '\n\n\n-------------------'
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# print myFinalTree
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# # --------
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# # 模型树求解
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# myDat = loadDataSet('input/9.RegTrees/data4.txt')
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# myMat = mat(myDat)
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# myTree = createTree(myMat, modelLeaf, modelErr)
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# print myTree
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# # 回归树 VS 模型树 VS 线性回归
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trainMat = mat(loadDataSet('input/9.RegTrees/bikeSpeedVsIq_train.txt'))
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testMat = mat(loadDataSet('input/9.RegTrees/bikeSpeedVsIq_test.txt'))
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# # 回归树
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# myTree1 = createTree(trainMat, ops=(1, 20))
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# print myTree1
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# yHat1 = createForeCast(myTree1, testMat[:, 0])
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# print "回归树:", corrcoef(yHat1, testMat[:, 1],rowvar=0)[0, 1]
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# 模型树
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myTree2 = createTree(trainMat, modelLeaf, modelErr, ops=(1, 20))
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yHat2 = createForeCast(myTree2, testMat[:, 0], modelTreeEval)
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print myTree2
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print "模型树:", corrcoef(yHat2, testMat[:, 1],rowvar=0)[0, 1]
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# 线性回归
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ws, X, Y = linearSolve(trainMat)
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print ws
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m = len(testMat[:, 0])
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yHat3 = mat(zeros((m, 1)))
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for i in range(shape(testMat)[0]):
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yHat3[i] = testMat[i, 0]*ws[1, 0] + ws[0, 0]
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print "线性回归:", corrcoef(yHat3, testMat[:, 1],rowvar=0)[0, 1]
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