笔记见备注
1 # _*_ coding:utf-8 _*_ 2 from numpy import * 3 # 简单数据集 4 def loadSimpData(): 5 datMat = matrix([[1., 2.1], 6 [2., 1.1], 7 [1.3, 1.], 8 [1., 1.], 9 [2., 1.]]) 10 11 classLabels = [1.0, 1.0, -1.0, -1.0, 1.0] 12 return datMat, classLabels 13 14 # 7-1 单层决策树生成函数 15 16 # lt=less than 17 # 分类器的构建(单纯地将某一特征上的所有取值与输入的阈值进行比较，若制定lt为负，则特征值小于阈值的样本被标记为-1) 18 # 相反而知，若指定gt为负，则特征值大于阈值的样本被标记为-1 19 def stumpClassify(dataMatrix, dimen, threshVal, threshIneq): 20 retArray = ones((shape(dataMatrix)[0],1)) 21 if threshIneq == 'lt': 22 retArray[dataMatrix[:, dimen] <= threshVal] = -1.0 23 else: 24 retArray[dataMatrix[:, dimen] > threshVal] = -1.0 25 return retArray 26 27 # stumpClassify分类器的预测值收到了特征、阈值和阈值两边到底哪边为正标签哪边为父标签的影响 28 # 所以有三重循环 29 # 第一重：遍历每个特征 30 # 第二重：对每个特征上依次设定不同的阈值 31 # 第三重：每个特征的每个阈值设定以后 还要依次以小、大于阈值作为依据调用分类器。得出预测结果。将结果与真实结果对比，得出错误向量 32 # 通过错误向量得出加权错误值之后与当前的最小错误值进行对比，迭代后得到最终的最小错误 33 def buildStump(dataArr, classLabels, D): 34 dataMatrix = mat(dataArr) 35 labelMat = mat(classLabels).T 36 m,n = shape(dataMatrix) 37 numSteps = 10.0 # 也可以变大，使得阈值的精确度更高，但是会造成计算量的增大 38 bestStump = {} 39 bestClasEst = mat(zeros((m,1))) 40 minError = inf 41 for i in range(n): 42 rangeMin = dataMatrix[:,i].min() 43 rangeMax = dataMatrix[:,i].max() 44 stepSize = (rangeMax - rangeMin)/numSteps 45 for j in range(-1, int(numSteps)+1): # 为什么从-1开始？？？？ 46 for inequal in ['lt','gt']: 47 threshVal = (rangeMin + float(j)*stepSize) 48 predictedVals = stumpClassify(dataMatrix, i, threshVal, inequal) 49 errArr = mat(ones((m, 1))) 50 errArr[predictedVals == labelMat] = 0 51 weightedError = D.T * errArr 52 # print ("split: dim %d, thresh %.2f, thresh ineqal: %s, the weighted error is %.3f" 53 # %(i, threshVal, inequal, weightedError)) 54 if weightedError < minError: 55 minError = weightedError 56 bestClasEst = predictedVals.copy() 57 bestStump['dim'] = i 58 bestStump['thresh'] = threshVal 59 bestStump['ineq'] = inequal 60 return bestStump, minError, bestClasEst # 单层决策树建立出来之后，需要知道的是最好的决策树（是的预测值的加权错误最小的树）的、 61 # 特征、阈值、约定的负标签方向；最小错误值；最好的预测结果（一个以样本个数为维度的向量） 62 63 64 65 66 # 7-2 基于单层决策树的AdaBoost训练过程 67 def adaBoostTrainDS(dataArr, classLabels, numIt=40): 68 weakClassArr = [] 69 m = shape(dataArr)[0] 70 D = mat(ones((m,1))/m) 71 aggClassEst = mat(zeros((m,1))) 72 for i in range(numIt): 73 bestStump, error, classEst = buildStump(dataArr, classLabels, D) 74 print ("D:", D.T) 75 alpha = float(0.5*log((1.0-error)/max(error,1e-16))) # 避免没有错误是发生溢出 76 bestStump['alpha'] = alpha 77 weakClassArr.append(bestStump) 78 print ("classEst: ", classEst.T) 79 expon = multiply(-1*alpha*mat(classLabels).T, classEst) 80 D = multiply(D, exp(expon)) 81 D = D/D.sum() 82 aggClassEst += alpha*classEst 83 print ("aggClassEst: ",aggClassEst.T) 84 aggErrors = multiply(sign(aggClassEst) != mat(classLabels).T, ones((m,1))) #ones zeros的（）里面一定不能忘了是元祖，而不是两个数 85 errorRate = aggErrors.sum()/m 86 print ("total error: ", errorRate, " ") 87 if errorRate == 0.0: break 88 return weakClassArr