基于SVM手写数字识别
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代码链接：http://download.csdn.net/detail/edwards_june/9856050
from numpy import *def loadDataSet(fileName): dataMat = [] labelMat = [] fr = open(fileName) for line in fr.readlines(): lineArr = line.strip().split('\t') dataMat.append([float(lineArr[0]), float(lineArr[1])]) labelMat.append(float(lineArr[2])) return dataMat, labelMatdef selectJrand(i, m): j = i while (j == i): j = int(random.uniform(0, m)) return j# 调整alpha值def clipAlpha(aj, H, L): if aj > H: aj = H if L > aj: aj = L return ajdef smoSimple(dataMatIn, classLabels, C, toler, maxIter): dataMatrix = mat(dataMatIn) labelMat = mat(classLabels).transpose() b = 0 m, n = shape(dataMatrix) alphas = mat(zeros((m, 1))) iter = 0 while (iter < maxIter): alphaPairsChanged = 0 for i in range(m): fXi = float(multiply(alphas, labelMat).T * (dataMatrix * dataMatrix[i, :].T)) + b Ei = fXi - float(labelMat[i]) if ((labelMat[i] * Ei < -toler) and (alphas[i] < C)) or ((labelMat[i] * Ei > toler) and (alphas[i] > 0)): j = selectJrand(i, m) # 从0到m选出不等于i的随机数 fXj = float(multiply(alphas, labelMat).T * (dataMatrix * dataMatrix[j, :].T)) + b Ej = fXj - float(labelMat[j]) alphaIold = alphas[i].copy() alphaJold = alphas[j].copy() if (labelMat[i] != labelMat[j]): L = max(0, alphas[j] - alphas[i]) H = min(C, C + alphas[j] - alphas[i]) else: L = max(0, alphas[j] + alphas[i] - C) H = min(C, alphas[j] + alphas[i]) if L == H: print("L==H") continue eta = 2.0 * dataMatrix[i, :] * dataMatrix[j, :].T \ - dataMatrix[i, :] * dataMatrix[i, :].T \ - dataMatrix[j, :] * dataMatrix[j, :].T if eta >= 0: print("eta>=0") continue alphas[j] -= labelMat[j] * (Ei - Ej) / eta alphas[j] = clipAlpha(alphas[j], H, L) if (abs(alphas[j] - alphaJold) < 0.00001): print("j not moving enough") continue alphas[i] += labelMat[j] * labelMat[i] * (alphaJold - alphas[j]) b1 = b - Ei - labelMat[i] * (alphas[i] - alphaIold) * dataMatrix[i, :] * dataMatrix[i, :].T - labelMat[ j] * ( alphas[ j] - alphaJold) * dataMatrix[ i, :] * dataMatrix[ j, :].T b2 = b - Ej - labelMat[i] * (alphas[i] - alphaIold) * dataMatrix[i, :] * dataMatrix[j, :].T - labelMat[ j] * ( alphas[ j] - alphaJold) * dataMatrix[ j, :] * dataMatrix[ j, :].T if (0 < alphas[i]) and (C > alphas[i]): b = b1 elif (0 < alphas[j]) and (C > alphas[j]): b = b2 else: b = (b1 + b2) / 2.0 alphaPairsChanged += 1 print("iter: %d i: %d, pairs changed %d" % (iter, i, alphaPairsChanged)) if (alphaPairsChanged == 0): iter += 1 else: iter = 0 print("iteration number: %d" % iter) return b, alphas# begin 完整版Platt SMO支持函数class optStruct: def __init__(self, dataMatIn, classLabels, C, toler): self.X = dataMatIn self.labelMat = classLabels self.C = C self.tol = toler self.m = shape(dataMatIn)[0] self.alphas = mat(zeros((self.m, 1))) self.b = 0 self.eCache = mat(zeros((self.m, 2)))def calcEk(oS, k): # fXk = float(multiply(oS.alphas, oS.labelMat).T * (oS.X * oS.X[k, :].T)) + oS.b fXk = float(multiply(oS.alphas, oS.labelMat).T * oS.K[:, k] + oS.b) Ek = fXk - float(oS.labelMat[k]) return Ekdef selectJ(i, oS, Ei): maxK = -1 maxDeltaE = 0 Ej = 0 oS.eCache[i] = [1, Ei] validEcacheList = nonzero(oS.eCache[:, 0].A)[0] if (len(validEcacheList)) > 1: for k in validEcacheList: if k == i: continue Ek = calcEk(oS, k) deltaE = abs(Ei - Ek) if (deltaE > maxDeltaE): maxK = k maxDeltaE = deltaE Ej = Ek return maxK, Ej else: j = selectJrand(i, oS.m) Ej = calcEk(oS, j) return j, Ejdef updateEk(oS, k): Ek = calcEk(oS, k) oS.eCache[k] = [1, Ek]# end 完整版Platt SMO支持函数# 完整Platt SMO优化例程def innerL(i, oS): Ei = calcEk(oS, i) if ((oS.labelMat[i] * Ei < -oS.tol) and (oS.alphas[i] < oS.C)) or ( (oS.labelMat[i] * Ei > oS.tol) and (oS.alphas[i] > 0)): j, Ej = selectJ(i, oS, Ei) alphaIold = oS.alphas[i].copy() alphaJold = oS.alphas[j].copy() if (oS.labelMat[i] != oS.labelMat[j]): L = max(0, oS.alphas[j] - oS.alphas[i]) H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i]) else: L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C) H = min(oS.C, oS.alphas[j] + oS.alphas[i]) if L == H: print("L==H"); return 0 # eta = 2.0 * oS.X[i, :] * oS.X[j, :].T - oS.X[i, :] * oS.X[i, :].T - oS.X[j, :] * oS.X[j, :].T eta = 2.0 * oS.K[i, j] - oS.K[i, i] - oS.K[j, j] if eta >= 0: print("eta>=0"); return 0 oS.alphas[j] -= oS.labelMat[j] * (Ei - Ej) / eta oS.alphas[j] = clipAlpha(oS.alphas[j], H, L) updateEk(oS, j) if (abs(oS.alphas[j] - alphaJold) < 0.00001): print("j not moving enough") return 0 oS.alphas[i] += oS.labelMat[j] * oS.labelMat[i] * (alphaJold - oS.alphas[j]) updateEk(oS, j) # b1 = oS.b - Ei - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.X[i, :] * oS.X[i, :].T - oS.labelMat[j] * ( # oS.alphas[j] - alphaJold) * oS.X[i, :] * oS.X[j, :].T # b2 = oS.b - Ej - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.X[i, :] * oS.X[j, :].T - oS.labelMat[j] * ( # oS.alphas[j] - alphaJold) * oS.X[j, :] * oS.X[j, :].T b1 = oS.b - Ei - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.K[i, i] - oS.labelMat[j] * ( oS.alphas[j] - alphaJold) * oS.K[i, j] b2 = oS.b - Ej - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.K[i, j] - oS.labelMat[j] * ( oS.alphas[j] - alphaJold) * oS.K[j, j] if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]): oS.b = b1 elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]): oS.b = b2 else: oS.b = (b1 + b2) / 2.0 return 1 else: return 0# 完整版Platt SMO 外循环代码def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)): oS = optStruct(mat(dataMatIn), mat(classLabels).transpose(), C, toler, kTup) iter = 0 entireSet = True alphaPairsChanged = 0 while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)): alphaPairsChanged = 0 if entireSet: for i in range(oS.m): alphaPairsChanged += innerL(i, oS) print("fullSet, iter: %d i %d, pairs changed %d" % (iter, i, alphaPairsChanged)) iter += 1 else: nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0] for i in nonBoundIs: alphaPairsChanged += innerL(i, oS) print("non-bound, iter: %d i %d, pairs changed %d" % (iter, i, alphaPairsChanged)) iter += 1 if entireSet: entireSet = False elif (alphaPairsChanged == 0): entireSet = True print("iteration number: %d" % iter) return oS.b, oS.alphasdef calcWs(alphas, dataArr, classLabels): X = mat(dataArr) labelMat = mat(classLabels).transpose() m, n = shape(X) w = zeros((n, 1)) for i in range(m): w += multiply(alphas[i] * labelMat[i], X[i, :].T) return w#核转换函数def kernelTrans(X, A, kTup): m, n = shape(X) K = mat(zeros((m, 1))) if kTup[0] == 'lin': K = X * A.T elif kTup[0] == 'rbf': for j in range(m): deltaRow = X[j, :] - A K[j] = deltaRow * deltaRow.T K = exp(K / (-1 * kTup[1] ** 2)) else: raise NameError('Houson We Have a Problem-- That Kernel is not recognzed') return Kclass optStruct: def __init__(self, dataMatIn, classLabels, C, toler, kTup): self.X = dataMatIn self.labelMat = classLabels self.C = C self.tol = toler self.m = shape(dataMatIn)[0] self.alphas = mat(zeros((self.m, 1))) self.b = 0 self.eCache = mat(zeros((self.m, 2))) self.K = mat(zeros((self.m, self.m))) for i in range(self.m): self.K[:, i] = kernelTrans(self.X, self.X[i, :], kTup)# 利用核函数进行分类的径向基测试函数def testRbf(k1=1.3): dataArr, labelArr = loadDataSet('testSetRBF.txt') b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) datMat = mat(dataArr) labelMat = mat(labelArr).transpose() svInd = nonzero(alphas.A > 0)[0] sVs = datMat[svInd] labelSV = labelMat[svInd] print("there are %d Support Vectors" % shape(sVs)[0]) m, n = shape(datMat) errorCount = 0 for i in range(m): kernelEval = kernelTrans(sVs, datMat[i, :], ('rbf', k1)) predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b if sign(predict) != sign(labelArr[i]): errorCount += 1 print("the training error rate is: %f" % (float(errorCount) / m)) dataArr, labelArr = loadDataSet('testSetRBF2.txt') errorCount = 0 datMat = mat(dataArr) labelMat = mat(labelArr).transpose() m, n = shape(datMat) for i in range(m): kernelEval = kernelTrans(sVs, datMat[i, :], ('rbf', k1)) predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b if sign(predict) != sign(labelArr[i]): errorCount += 1 print("the test error rate is: %f" % (float(errorCount) / m))##################手写识别问题##基于SVM手写数字识别#################def img2vector(filename): returnVect = zeros((1,1024)) fr = open(filename) for i in range(32): lineStr = fr.readline() for j in range(32): returnVect[0,32*i+j] = int(lineStr[j]) return returnVectdef loadImages(dirName): from os import listdir hwLabels = [] trainingFileList = listdir(dirName) m = len(trainingFileList) trainingMat = zeros((m, 1024)) for i in range(m): fileNameStr = trainingFileList[i] fileStr = fileNameStr.split('.')[0] classNumStr = int(fileStr.split('_')[0]) if classNumStr == 9:hwLabels.append(-1) else: hwLabels.append(1) trainingMat[i,:] = img2vector('%s/%s' %(dirName, fileNameStr)) return trainingMat, hwLabelsdef testDigits(kTup = ('rbf', 10)): dataArr, labelArr = loadImages('trainingDigits') b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTup) datMat = mat(dataArr) labelMat = mat(labelArr).transpose() svInd = nonzero(alphas.A>0)[0] sVs = datMat[svInd] labelSV = labelMat[svInd] print("there are %d Support Vector" %shape(sVs)[0]) m, n = shape(datMat) errorCount = 0 for i in range(m): kernelEval = kernelTrans(sVs, datMat[i,:], kTup) predict = kernelEval.T * multiply(labelSV, alphas[svInd])+b if sign(predict) != sign(labelArr[i]): errorCount+=1 print("the training error rate is: %f"%(float(errorCount)/m)) dataArr, labelArr = loadImages('testDigits') errorCount =0 datMat =mat(dataArr) labelMat = mat(labelArr).transpose() m, n = shape(datMat) for i in range(m): kernelEval = kernelTrans(sVs, datMat[i,:], kTup) predict = kernelEval.T * multiply(labelSV, alphas[svInd])+b if sign(predict) != sign(labelArr[i]): errorCount += 1 print("the test error rate is :%f"%(float(errorCount)/m))阅读全文
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