Merge branch 'master' of https://github.com/apachecn/MachineLearning

# Conflicts:
#	docs/5.Logistic回归.md

README.md

@@ -1,6 +1,6 @@
 # MachineLearning
 
-**Mahchine Leaning in Action (python)**
+**Mahchine Leaning in Action (python) | [ApacheCN(apache中文网)](http://www.apache.wiki/display/ML)**
 
 ## 第一部分  分类
 
@@ -20,6 +20,7 @@
 
 * 8) 预测数值型数据：回归
 * 9) 数回归
+    * [树回归](./docs/9.树回归.md)
 
 ## 第三部分  无监督学习
 
@@ -32,7 +33,7 @@
 ## 第四部分  其他工具
 
 * 13) 使用PCA来简化数据
-     *[利用PCA来简化数据](./docs/13.利用PCA来简化数据.md)
+    * [利用PCA来简化数据](./docs/13.利用PCA来简化数据.md)
 * 14) 使用SVD简化数据
 * 15) 大数据与MapReduce
 
@@ -44,3 +45,4 @@
 * 附录D 资源
 * 索引
 * 版权声明
+* [ApacheCN(apache中文网) 维护更新](http://www.apache.wiki/display/ML)

docs/1.机器学习基础.md

@@ -5,6 +5,8 @@
     * 把无序的数据转换成有用的信息。
 * 机器学习的意义
     * 我们利用计算机来彰显数据背后的真实含义。
+* 机器学习的任务
+    * 机器学习的主要任务就是分类。
 * 监督学习
     * 样本集：训练数据 + 测试数据
     * 特征(feature-是否有缺失情况) + 目标变量(分类-离散值<A/B/C、 是/否>/回归-连续值<0~100、 -999～999>)

docs/3.决策树.md

@@ -23,3 +23,5 @@
             * \\(H = -\sum_{i=0}^np(x_i)\log_2p(x_i)\\) 表示香农熵，用于计算信息熵
     * 基尼不纯度(Gini impurity)  [本书不做过多的介绍]
         * 简单来说：就是从一个数据集中随机选取子项，度量其被错误分类到其他分组里的概率。
+* 流程介绍图
+* ![决策树流程介绍图](./3.决策树流程介绍图.jpg)

docs/9.树回归.md

@@ -0,0 +1,13 @@
+
+# 9) 树回归
+
+* 树回归是什么？
+    * 分类回归树(Classification and Regression Tree，CART)是一种典型的决策树算法，CART算法不仅可以应用于分类问题，而且可以用于回归问题。
+    * CART算法构建的回归树并介绍其中的树剪枝技术(该技术主要的目的是防止数的过拟合)
+* 树回归的构建
+    * 优点：可以对复杂和非线性的数据建模。
+    * 缺点：结果不易理解。
+    * 适用数据类型：数值型和标称型数据。
+* 那么问题来了，如何计算连续型数值的混乱度呢？
+    * `误差`：也就是计算平均差的总值(总方差=方差*样本数)
+    * 二元切分方式

src/python/01.NumPy.py

@@ -20,10 +20,15 @@ randArray = random.rand(4, 4)
 
 # 转化关系， 数组转化为矩阵
 randMat = mat(randArray)
-# .I表示对矩阵求逆
+# .I表示对矩阵求逆(可以利用矩阵的初等变换
+#    # 意义：逆矩阵是一个判断相似性的工具。逆矩阵A与列向量p相乘后，将得到列向量q，q的第i个分量表示p与A的第i个列向量的相似度。
+#    # 参考案例链接：
+#    # https://www.zhihu.com/question/33258489
+#    # http://blog.csdn.net/vernice/article/details/48506027
+# .T表示对矩阵转置(行列颠倒)
 invRandMat = randMat.I
 # 输出结果
-print randArray, '\n', randMat, '\n', invRandMat
+print randArray, '\n---\n', randMat, '\n+++\n', invRandMat
 # 矩阵和逆矩阵 进行求积 (单位矩阵，对角线都为1嘛，理论上4*4的矩阵其他的都为0)
 myEye = randMat*invRandMat
 # 误差

src/python/03.DecisionTree/DTSklearn.py

@@ -104,6 +104,7 @@ def show_pdf(clf):
     # from IPython.display import Image
     # Image(graph.create_png())
 
+
 if __name__ == '__main__':
     x, y = createDataSet()
 

src/python/03.DecisionTree/DecisionTreePlot.py

@@ -77,9 +77,9 @@ def plotTree(myTree, parentPt, nodeTxt):
     plotTree.yOff = plotTree.yOff - 1.0/plotTree.totalD
     for key in secondDict.keys():
         # 判断该节点是否是Node节点
-        if type(secondDict[key]).__name__=='dict':
+        if type(secondDict[key]).__name__ == 'dict':
             # 如果是就递归调用[recursion]
-            plotTree(secondDict[key],cntrPt,str(key))
+            plotTree(secondDict[key], cntrPt, str(key))
         else:
             # 如果不是，就在原来节点一半的地方找到节点的坐标
             plotTree.xOff = plotTree.xOff + 1.0/plotTree.totalW
@@ -121,7 +121,7 @@ def createPlot(inTree):
 
 # 测试数据集
 def retrieveTree(i):
-    listOfTrees =[
+    listOfTrees = [
         {'no surfacing': {0: 'no', 1: {'flippers': {0: 'no', 1: 'yes'}}}},
         {'no surfacing': {0: 'no', 1: {'flippers': {0: {'head': {0: 'no', 1: 'yes'}}, 1: 'no'}}}}
     ]

src/python/09.RegTrees/TreeNode.py

@@ -0,0 +1,16 @@
+#!/usr/bin/python
+# coding:utf8
+
+'''
+Created on 2017-03-06
+Update on 2017-03-06
+@author: jiangzhonglian
+'''
+
+
+class treeNode():
+    def __init__(self, feat, val, right, left):
+        self.featureToSplitOn = feat
+        self.valueOfSplit = val
+        self.rightBranch = right
+        self.leftBranch = left

src/python/09.RegTrees/regTrees.py

@@ -0,0 +1,324 @@
+#!/usr/bin/python
+# coding:utf8
+
+'''
+Created on Feb 4, 2011
+Update on 2017-03-02
+Tree-Based Regression Methods Source Code for Machine Learning in Action Ch. 9
+@author: Peter Harrington/jiangzhonglian
+'''
+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 数据集
+        leafType 计算叶子节点的函数
+        errType 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):
+        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)):
+    # 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
+    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
+    if shape(testData)[0] == 0:
+        return getMean(tree)
+    # 对测试进行分支，看属于哪只分支，然后返回tree结果的均值
+    if (isTree(tree['right']) or isTree(tree['left'])):
+        lSet, rSet = binSplitDataSet(testData, tree['spInd'], tree['spVal'])
+    if isTree(tree['left']):
+        tree['left'] = prune(tree['left'], lSet)
+    if isTree(tree['right']):
+        tree['right'] = prune(tree['right'], rSet)
+
+    # 如果左右两边无子分支，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
+    # 1.如果测试数据集足够大，将tree进行分支到最后
+    # 2.如果测试数据集不够大，那么就无法进行合并
+    # 注意返回的结果： 是合并后对原来为字典tree进行赋值，相当于进行了合并
+    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
+    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('testData/RT_data1.txt')
+    # myDat = loadDataSet('testData/RT_data2.txt')
+    # myMat = mat(myDat)
+    # myTree = createTree(myMat)
+
+    # 1. 预剪枝就是，提起设置最大误差数和最少元素数
+    # myDat = loadDataSet('testData/RT_data3.txt')
+    # myMat = mat(myDat)
+    # myTree = createTree(myMat, ops=(0, 1))
+    # print myTree
+
+    # 2.后剪枝
+    # myDatTest = loadDataSet('testData/RT_data3test.txt')
+    # myMat2Test = mat(myDatTest)
+    # myFinalTree = prune(myTree, myMat2Test)
+    # print '\n\n\n-------------------'
+    # print myFinalTree
+
+    # --------
+    # 模型树求解
+    # myDat = loadDataSet('testData/RT_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('testData/RT_bikeSpeedVsIq_train.txt'))
+    testMat = mat(loadDataSet('testData/RT_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]

src/python/regression.py

@@ -11,6 +11,7 @@ import os
 from numpy import *
 import matplotlib.pylab as plt
 
+
 def loadDataSet(fileName):      #general function to parse tab -delimited floats
     numFeat = len(open(fileName).readline().split('\t')) - 1 #get number of fields
     dataMat = []; labelMat = []
@@ -24,6 +25,7 @@ def loadDataSet(fileName):      #general function to parse tab -delimited floats
         labelMat.append(float(curLine[-1]))
     return dataMat,labelMat
 
+
 def standRegres(xArr,yArr):
     # >>> A.T  # transpose, 转置
     xMat = mat(xArr); yMat = mat(yArr).T
@@ -37,6 +39,7 @@ def standRegres(xArr,yArr):
     ws = xTx.I * (xMat.T*yMat)  # 最小二乘法求最优解
     return ws
 
+
 def plotBestFit(xArr, yArr, ws):
 
     xMat = mat(xArr)
@@ -60,6 +63,7 @@ def plotBestFit(xArr, yArr, ws):
     plt.xlabel('X'); plt.ylabel('Y')
     plt.show()
 
+
 def main1():
     # w0*x0+w1*x1+w2*x2=f(x)
     project_dir = os.path.dirname(os.path.dirname(os.getcwd()))
@@ -91,6 +95,7 @@ def lwlr(testPoint, xArr, yArr,k=1.0):
     ws = xTx.I * (xMat.T * (weights * yMat))
     return testPoint * ws
 
+
 def lwlrTest(testArr,xArr,yArr,k=1.0):  #loops over all the data points and applies lwlr to each one
     m = shape(testArr)[0]
     # m*1的矩阵
@@ -101,6 +106,7 @@ def lwlrTest(testArr,xArr,yArr,k=1.0):  #loops over all the data points and appl
         yHat[i] = lwlr(testArr[i],xArr,yArr,k)
     return yHat
 
+
 def lwlrTestPlot(xArr, yArr, yHat):
 
     xMat = mat(xArr)
@@ -123,11 +129,13 @@ def lwlrTestPlot(xArr, yArr, yHat):
     plt.xlabel('X'); plt.ylabel('Y')
     plt.show()
 
+
 def main2():
     # w0*x0+w1*x1+w2*x2=f(x)
-    project_dir = os.path.dirname(os.path.dirname(os.getcwd()))
+    # project_dir = os.path.dirname(os.path.dirname(os.getcwd()))
     # 1.收集并准备数据
-    xArr, yArr = loadDataSet("%s/resources/ex0.txt" % project_dir)
+    # xArr, yArr = loadDataSet("%s/resources/ex0.txt" % project_dir)
+    xArr, yArr = loadDataSet("testData/Regression_data.txt")
     # print xArr, '---\n', yArr
     # 2.训练模型，  f(x)=a1*x1+b2*x2+..+nn*xn中 (a1,b2, .., nn).T的矩阵值
     yHat = lwlrTest(xArr, xArr, yArr, 0.003)
@@ -136,12 +144,14 @@ def main2():
     # 数据可视化
     lwlrTestPlot(xArr, yArr, yHat)
 
-if __name__=="__main__":
+
+if __name__ == "__main__":
     # 线性回归
     # main1()
     # 局部加权线性回归
     main2()
 
+
 def rssError(yArr,yHatArr): #yArr and yHatArr both need to be arrays
     return ((yArr-yHatArr)**2).sum()
 

testData/RT_bikeSpeedVsIq_test.txt

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testData/RT_bikeSpeedVsIq_train.txt

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testData/RT_data1.txt

@@ -0,0 +1,200 @@
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testData/RT_data2.txt

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testData/RT_data3.txt

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testData/RT_data3test.txt

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testData/RT_data4.txt

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testData/Regression_data.txt

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