之前学习Java的时候，用过一个IDE叫做EditPlus,虽然他敲代码的高亮等体验度不及eclipse，但是打开软件特别快捷，现在也用他读python特别方便。
训练算法:：使用梯度上升找到最佳参数
之前看过吴恩达的视频的同学们，听得比较多的就是梯度下降算法，但是梯度上升算法和梯度下降算法本质是是一样的，只是梯度计算的时候加减号不一样罢了。
1 def loadDataSet():
2 dataMat = []; labelMat = []
3 fr = open('testSet.txt')
4 for line in fr.readlines():
5 lineArr = line.strip().split()
6 dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])
7 labelMat.append(int(lineArr[2]))
8 return dataMat,labelMat
9
10 def sigmoid(inX):
11 return 1.0/(1+exp(-inX))
12
13 def gradAscent(dataMatIn, classLabels):
14 dataMatrix = mat(dataMatIn) #convert to NumPy matrix
15 labelMat = mat(classLabels).transpose() #convert to NumPy matrix
16 m,n = shape(dataMatrix)
17 alpha = 0.001
18 maxCycles = 500
19 weights = ones((n,1))
20 for k in range(maxCycles): #heavy on matrix operations
21 h = sigmoid(dataMatrix*weights) #matrix mult
22 error = (labelMat - h) #vector subtraction
23 weights = weights + alpha * dataMatrix.transpose()* error #matrix mult
24 return weights
第一个函数打开testSet。txt并逐行读取，每行前两个值分别是x1和x2，第三个值是对应的类别标签。为了方便计算，该函数还将x0的值设为1.0
第二个函数是sigmoid函数，x为0时，函数值为0.5，x增大时，函数值将不断增大逼近1。
第三个函数有两个参数，第一个是2维数组，每列代表不同的特征，每行代表每个训练样本。我们采用100个样本的简单数据集它包含两个特征x1,x2，再加上第0维特征x0,所以dataMatln里面存放的是100*3的矩阵。
分析数据：画出决策边界
1 def plotBestFit(weights):
2 import matplotlib.pyplot as plt
3 dataMat,labelMat=loadDataSet()
4 dataArr = array(dataMat)
5 n = shape(dataArr)[0]
6 xcord1 = []; ycord1 = []
7 xcord2 = []; ycord2 = []
8 for i in range(n):
9 if int(labelMat[i])== 1:
10 xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2])
11 else:
12 xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2])
13 fig = plt.figure()
14 ax = fig.add_subplot(111)
15 ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')
16 ax.scatter(xcord2, ycord2, s=30, c='green')
17 x = arange(-3.0, 3.0, 0.1)
18 y = (-weights[0]-weights[1]*x)/weights[2]
19 ax.plot(x, y)
20 plt.xlabel('X1'); plt.ylabel('X2');
21 plt.show()
>>> from numpy import *
>>> reload(logRegres)
<module 'logRegres' from 'D:\Python27\logRegres.pyc'>
>>> weights=logRegres.gradAscent(dataArr,labelMat)
>>> logRegres.plotBestFit(weights.getA())
训练算法：随机梯度上升
梯度上升算法在每次更新回归系数时都需要遍历整个数据集。改进的方法是一次仅使用一个样本点来更新回归系数，该方法称为随机梯度上升算法。由于可以在样本到来时对分类器进行增量式更新，因而随机梯度上升算法是一个在线学习算法。与在线学习相对应，一次处理所有数据被称作是批处理。
1 def stocGradAscent0(dataMatrix, classLabels):
2 m,n = shape(dataMatrix)
3 alpha = 0.01
4 weights = ones(n) #initialize to all ones
5 for i in range(m):
6 h = sigmoid(sum(dataMatrix[i]*weights))
7 error = classLabels[i] - h
8 weights = weights + alpha * error * dataMatrix[i]
9 return weights
>>> from numpy import *
>>> reload(logRegres)
<module 'logRegres' from 'D:\Python27\logRegres.pyc'>
>>> dataArr,labelMat=logRegres.loadDataSet()
>>> weights=logRegres.stocGradAscent0(array(dataArr),labelMat)
>>> logRegres.plotBestFit(weights)
改进的随机梯度上升算法
1 def stocGradAscent1(dataMatrix, classLabels, numIter=150):
2 m,n = shape(dataMatrix)
3 weights = ones(n) #initialize to all ones
4 for j in range(numIter):
5 dataIndex = range(m)
6 for i in range(m):
7 alpha = 4/(1.0+j+i)+0.0001 #apha decreases with iteration, does not
8 randIndex = int(random.uniform(0,len(dataIndex)))#go to 0 because of the constant
9 h = sigmoid(sum(dataMatrix[randIndex]*weights))
10 error = classLabels[randIndex] - h
11 weights = weights + alpha * error * dataMatrix[randIndex]
12 del(dataIndex[randIndex])
13 return weights
增加了亮出代码来进行改进。一方面，alpha在每次迭代的时候都会调整，虽然alpha会随着迭代次数不断减小，但永远不会减小到0，因为存在一个常数项。
另一方面，通过随机选取样本来更新回归系数。
>>> dataArr,labelMat=logRegres.loadDataSet()
>>> weights=logRegres.stocGradAscent1(array(dataArr),labelMat)
>>> logRegres.plotBestFit(weights)
从疝气病症预测病马的死亡率
1 def classifyVector(inX, weights):
2 prob = sigmoid(sum(inX*weights))
3 if prob > 0.5: return 1.0
4 else: return 0.0
5
6 def colicTest():
7 frTrain = open('horseColicTraining.txt'); frTest = open('horseColicTest.txt')
8 trainingSet = []; trainingLabels = []
9 for line in frTrain.readlines():
10 currLine = line.strip().split('\t')
11 lineArr =[]
12 for i in range(21):
13 lineArr.append(float(currLine[i]))
14 trainingSet.append(lineArr)
15 trainingLabels.append(float(currLine[21]))
16 trainWeights = stocGradAscent1(array(trainingSet), trainingLabels, 1000)
17 errorCount = 0; numTestVec = 0.0
18 for line in frTest.readlines():
19 numTestVec += 1.0
20 currLine = line.strip().split('\t')
21 lineArr =[]
22 for i in range(21):
23 lineArr.append(float(currLine[i]))
24 if int(classifyVector(array(lineArr), trainWeights))!= int(currLine[21]):
25 errorCount += 1
26 errorRate = (float(errorCount)/numTestVec)
27 print "the error rate of this test is: %f" % errorRate
28 return errorRate
29
30 def multiTest():
31 numTests = 10; errorSum=0.0
32 for k in range(numTests):
33 errorSum += colicTest()
34 print "after %d iterations the average error rate is: %f" % (numTests, errorSum/float(numTests))
第一个函数，如果sigmoid值大于0.5函数返回1，否则返回0.
第二个函数，用于打开测试集和训练集，并对数据进行格式化处理的函数。
第三个函数，调用第二个函数10次并求结果的平均值。
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