一、算法簡要

我們希望有這么一種函數：接受輸入然后預測出類別，這樣用于分類。這里，用到了數學中的sigmoid函數，sigmoid函數的具體表達式和函數圖象如下：

可以較為清楚的看到，當輸入的x小于0時，函數值<0.5，將分類預測為0；當輸入的x大于0時，函數值>0.5，將分類預測為1。

1.1 預測函數的表示

1.2參數的求解

二、代碼實現

函數sigmoid計算相應的函數值；gradAscent實現的batch-梯度上升，意思就是在每次迭代中所有數據集都考慮到了；而stoGradAscent0中，則是將數據集中的示例都比那里了一遍，復雜度大大降低；stoGradAscent1則是對隨機梯度上升的改進，具體變化是alpha每次變化的頻率是變化的，而且每次更新參數用到的示例都是隨機選取的。

from numpy import * import matplotlib.pyplot as plt def loadDataSet():   dataMat = []   labelMat = []   fr = open('testSet.txt')   for line in fr.readlines():     lineArr = line.strip('/n').split('/t')     dataMat.append([1.0, float(lineArr[0]), float(lineArr[1])])     labelMat.append(int(lineArr[2]))   fr.close()   return dataMat, labelMat def sigmoid(inX):   return 1.0/(1+exp(-inX)) def gradAscent(dataMatIn, classLabels):   dataMatrix = mat(dataMatIn)   labelMat = mat(classLabels).transpose()   m,n=shape(dataMatrix)   alpha = 0.001   maxCycles = 500   weights = ones((n,1))   errors=[]   for k in range(maxCycles):     h = sigmoid(dataMatrix*weights)     error = labelMat - h     errors.append(sum(error))     weights = weights + alpha*dataMatrix.transpose()*error   return weights, errors def stoGradAscent0(dataMatIn, classLabels):   m,n=shape(dataMatIn)   alpha = 0.01   weights = ones(n)   for i in range(m):     h = sigmoid(sum(dataMatIn[i]*weights))     error = classLabels[i] - h      weights = weights + alpha*error*dataMatIn[i]   return weights def stoGradAscent1(dataMatrix, classLabels, numIter = 150):   m,n=shape(dataMatrix)   weights = ones(n)   for j in range(numIter):     dataIndex=range(m)     for i in range(m):       alpha= 4/(1.0+j+i)+0.01       randIndex = int(random.uniform(0,len(dataIndex)))       h = sigmoid(sum(dataMatrix[randIndex]*weights))       error = classLabels[randIndex]-h       weights=weights+alpha*error*dataMatrix[randIndex]       del(dataIndex[randIndex])     return weights def plotError(errs):   k = len(errs)   x = range(1,k+1)   plt.plot(x,errs,'g--')   plt.show() def plotBestFit(wei):   weights = wei.getA()   dataMat, labelMat = loadDataSet()   dataArr = array(dataMat)   n = shape(dataArr)[0]   xcord1=[]   ycord1=[]   xcord2=[]   ycord2=[]   for i in range(n):      if int(labelMat[i])==1:       xcord1.append(dataArr[i,1])       ycord1.append(dataArr[i,2])     else:       xcord2.append(dataArr[i,1])       ycord2.append(dataArr[i,2])   fig = plt.figure()   ax = fig.add_subplot(111)   ax.scatter(xcord1, ycord1, s=30, c='red', marker='s')   ax.scatter(xcord2, ycord2, s=30, c='green')   x = arange(-3.0,3.0,0.1)   y=(-weights[0]-weights[1]*x)/weights[2]   ax.plot(x,y)   plt.xlabel('x1')   plt.ylabel('x2')   plt.show() def classifyVector(inX, weights):   prob = sigmoid(sum(inX*weights))   if prob>0.5:     return 1.0   else:     return 0 def colicTest(ftr, fte, numIter):   frTrain = open(ftr)   frTest = open(fte)   trainingSet=[]   trainingLabels=[]   for line in frTrain.readlines():     currLine = line.strip('/n').split('/t')     lineArr=[]     for i in range(21):       lineArr.append(float(currLine[i]))     trainingSet.append(lineArr)     trainingLabels.append(float(currLine[21]))   frTrain.close()   trainWeights = stoGradAscent1(array(trainingSet),trainingLabels, numIter)   errorCount = 0   numTestVec = 0.0   for line in frTest.readlines():     numTestVec += 1.0     currLine = line.strip('/n').split('/t')     lineArr=[]     for i in range(21):       lineArr.append(float(currLine[i]))     if int(classifyVector(array(lineArr), trainWeights))!=int(currLine[21]):       errorCount += 1   frTest.close()   errorRate = (float(errorCount))/numTestVec   return errorRate def multiTest(ftr, fte, numT, numIter):   errors=[]   for k in range(numT):     error = colicTest(ftr, fte, numIter)     errors.append(error)   print "There "+str(len(errors))+" test with "+str(numIter)+" interations in all!"   for i in range(numT):     print "The "+str(i+1)+"th"+" testError is:"+str(errors[i])   print "Average testError: ", float(sum(errors))/len(errors) ''''' data, labels = loadDataSet() weights0 = stoGradAscent0(array(data), labels) weights,errors = gradAscent(data, labels) weights1= stoGradAscent1(array(data), labels, 500) print weights plotBestFit(weights) print weights0 weights00 = [] for w in weights0:   weights00.append([w]) plotBestFit(mat(weights00)) print weights1 weights11=[] for w in weights1:   weights11.append([w]) plotBestFit(mat(weights11)) ''' multiTest(r"horseColicTraining.txt",r"horseColicTest.txt",10,500)