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jiangzhonglian
@@ -115,4 +115,358 @@ def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
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if (alphaPairsChanged == 0): iter += 1
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else: iter = 0
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print("iteration number: %d" % iter)
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return b,alphas
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return b,alphas
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def kernelTrans(X, A, kTup): # calc the kernel or transform data to a higher dimensional space
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m, n = shape(X)
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K = mat(zeros((m, 1)))
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if kTup[0] == 'lin':
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K = X * A.T # linear kernel
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elif kTup[0] == 'rbf':
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for j in range(m):
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deltaRow = X[j, :] - A
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K[j] = deltaRow * deltaRow.T
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K = exp(K / (-1 * kTup[1] ** 2)) # divide in NumPy is element-wise not matrix like Matlab
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else:
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raise NameError('Houston We Have a Problem -- \
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That Kernel is not recognized')
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return K
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class optStruct:
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def __init__(self, dataMatIn, classLabels, C, toler, kTup): # Initialize the structure with the parameters
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self.X = dataMatIn
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self.labelMat = classLabels
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self.C = C
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self.tol = toler
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self.m = shape(dataMatIn)[0]
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self.alphas = mat(zeros((self.m, 1)))
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self.b = 0
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self.eCache = mat(zeros((self.m, 2))) # first column is valid flag
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self.K = mat(zeros((self.m, self.m)))
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for i in range(self.m):
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self.K[:, i] = kernelTrans(self.X, self.X[i, :], kTup)
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def calcEk(oS, k):
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fXk = float(multiply(oS.alphas, oS.labelMat).T * oS.K[:, k] + oS.b)
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Ek = fXk - float(oS.labelMat[k])
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return Ek
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def selectJ(i, oS, Ei): # this is the second choice -heurstic, and calcs Ej
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maxK = -1
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maxDeltaE = 0
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Ej = 0
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oS.eCache[i] = [1, Ei] # set valid #choose the alpha that gives the maximum delta E
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validEcacheList = nonzero(oS.eCache[:, 0].A)[0]
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if (len(validEcacheList)) > 1:
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for k in validEcacheList: # loop through valid Ecache values and find the one that maximizes delta E
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if k == i: continue # don't calc for i, waste of time
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Ek = calcEk(oS, k)
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deltaE = abs(Ei - Ek)
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if (deltaE > maxDeltaE):
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maxK = k;
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maxDeltaE = deltaE;
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Ej = Ek
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return maxK, Ej
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else: # in this case (first time around) we don't have any valid eCache values
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j = selectJrand(i, oS.m)
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Ej = calcEk(oS, j)
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return j, Ej
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def updateEk(oS, k): # after any alpha has changed update the new value in the cache
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Ek = calcEk(oS, k)
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oS.eCache[k] = [1, Ek]
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def innerL(i, oS):
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Ei = calcEk(oS, i)
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if ((oS.labelMat[i] * Ei < -oS.tol) and (oS.alphas[i] < oS.C)) or (
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(oS.labelMat[i] * Ei > oS.tol) and (oS.alphas[i] > 0)):
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j, Ej = selectJ(i, oS, Ei) # this has been changed from selectJrand
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alphaIold = oS.alphas[i].copy();
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alphaJold = oS.alphas[j].copy();
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if (oS.labelMat[i] != oS.labelMat[j]):
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L = max(0, oS.alphas[j] - oS.alphas[i])
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H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i])
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else:
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L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C)
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H = min(oS.C, oS.alphas[j] + oS.alphas[i])
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if L == H: print
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"L==H";
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return 0
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eta = 2.0 * oS.K[i, j] - oS.K[i, i] - oS.K[j, j] # changed for kernel
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if eta >= 0: print
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"eta>=0";
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return 0
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oS.alphas[j] -= oS.labelMat[j] * (Ei - Ej) / eta
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oS.alphas[j] = clipAlpha(oS.alphas[j], H, L)
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updateEk(oS, j) # added this for the Ecache
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if (abs(oS.alphas[j] - alphaJold) < 0.00001): print
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"j not moving enough";
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return 0
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oS.alphas[i] += oS.labelMat[j] * oS.labelMat[i] * (alphaJold - oS.alphas[j]) # update i by the same amount as j
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updateEk(oS, i) # added this for the Ecache #the update is in the oppostie direction
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b1 = oS.b - Ei - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.K[i, i] - oS.labelMat[j] * (
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oS.alphas[j] - alphaJold) * oS.K[i, j]
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b2 = oS.b - Ej - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.K[i, j] - oS.labelMat[j] * (
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oS.alphas[j] - alphaJold) * oS.K[j, j]
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if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]):
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oS.b = b1
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elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]):
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oS.b = b2
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else:
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oS.b = (b1 + b2) / 2.0
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return 1
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else:
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return 0
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def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)): # full Platt SMO
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oS = optStruct(mat(dataMatIn), mat(classLabels).transpose(), C, toler, kTup)
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iter = 0
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entireSet = True;
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alphaPairsChanged = 0
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while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
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alphaPairsChanged = 0
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if entireSet: # go over all
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for i in range(oS.m):
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alphaPairsChanged += innerL(i, oS)
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print
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"fullSet, iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged)
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iter += 1
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else: # go over non-bound (railed) alphas
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nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
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for i in nonBoundIs:
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alphaPairsChanged += innerL(i, oS)
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print
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"non-bound, iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged)
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iter += 1
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if entireSet:
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entireSet = False # toggle entire set loop
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elif (alphaPairsChanged == 0):
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entireSet = True
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print
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"iteration number: %d" % iter
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return oS.b, oS.alphas
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def calcWs(alphas, dataArr, classLabels):
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X = mat(dataArr);
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labelMat = mat(classLabels).transpose()
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m, n = shape(X)
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w = zeros((n, 1))
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for i in range(m):
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w += multiply(alphas[i] * labelMat[i], X[i, :].T)
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return w
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def testRbf(k1=1.3):
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dataArr, labelArr = loadDataSet('testSetRBF.txt')
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b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) # C=200 important
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datMat = mat(dataArr);
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labelMat = mat(labelArr).transpose()
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svInd = nonzero(alphas.A > 0)[0]
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sVs = datMat[svInd] # get matrix of only support vectors
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labelSV = labelMat[svInd];
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print
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"there are %d Support Vectors" % shape(sVs)[0]
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m, n = shape(datMat)
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errorCount = 0
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for i in range(m):
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kernelEval = kernelTrans(sVs, datMat[i, :], ('rbf', k1))
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predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
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if sign(predict) != sign(labelArr[i]): errorCount += 1
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print
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"the training error rate is: %f" % (float(errorCount) / m)
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dataArr, labelArr = loadDataSet('testSetRBF2.txt')
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errorCount = 0
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datMat = mat(dataArr);
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labelMat = mat(labelArr).transpose()
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m, n = shape(datMat)
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for i in range(m):
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kernelEval = kernelTrans(sVs, datMat[i, :], ('rbf', k1))
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predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
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if sign(predict) != sign(labelArr[i]): errorCount += 1
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print
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"the test error rate is: %f" % (float(errorCount) / m)
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def img2vector(filename):
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returnVect = zeros((1, 1024))
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fr = open(filename)
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for i in range(32):
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lineStr = fr.readline()
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for j in range(32):
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returnVect[0, 32 * i + j] = int(lineStr[j])
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return returnVect
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def loadImages(dirName):
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from os import listdir
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hwLabels = []
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trainingFileList = listdir(dirName) # load the training set
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m = len(trainingFileList)
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trainingMat = zeros((m, 1024))
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for i in range(m):
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fileNameStr = trainingFileList[i]
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fileStr = fileNameStr.split('.')[0] # take off .txt
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classNumStr = int(fileStr.split('_')[0])
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if classNumStr == 9:
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hwLabels.append(-1)
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else:
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hwLabels.append(1)
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trainingMat[i, :] = img2vector('%s/%s' % (dirName, fileNameStr))
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return trainingMat, hwLabels
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def testDigits(kTup=('rbf', 10)):
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dataArr, labelArr = loadImages('trainingDigits')
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b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTup)
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datMat = mat(dataArr);
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labelMat = mat(labelArr).transpose()
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svInd = nonzero(alphas.A > 0)[0]
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sVs = datMat[svInd]
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labelSV = labelMat[svInd];
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print("there are %d Support Vectors" % shape(sVs)[0])
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m, n = shape(datMat)
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errorCount = 0
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for i in range(m):
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kernelEval = kernelTrans(sVs, datMat[i, :], kTup)
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predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
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if sign(predict) != sign(labelArr[i]): errorCount += 1
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print
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"the training error rate is: %f" % (float(errorCount) / m)
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dataArr, labelArr = loadImages('testDigits')
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errorCount = 0
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datMat = mat(dataArr);
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labelMat = mat(labelArr).transpose()
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m, n = shape(datMat)
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for i in range(m):
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kernelEval = kernelTrans(sVs, datMat[i, :], kTup)
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predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
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if sign(predict) != sign(labelArr[i]): errorCount += 1
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print
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"the test error rate is: %f" % (float(errorCount) / m)
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'''#######********************************
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Non-Kernel VErsions below
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''' #######********************************
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class optStructK:
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def __init__(self, dataMatIn, classLabels, C, toler): # Initialize the structure with the parameters
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self.X = dataMatIn
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self.labelMat = classLabels
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self.C = C
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self.tol = toler
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self.m = shape(dataMatIn)[0]
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self.alphas = mat(zeros((self.m, 1)))
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self.b = 0
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self.eCache = mat(zeros((self.m, 2))) # first column is valid flag
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def calcEkK(oS, k):
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fXk = float(multiply(oS.alphas, oS.labelMat).T * (oS.X * oS.X[k, :].T)) + oS.b
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Ek = fXk - float(oS.labelMat[k])
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return Ek
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def selectJK(i, oS, Ei): # this is the second choice -heurstic, and calcs Ej
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maxK = -1
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maxDeltaE = 0
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Ej = 0
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oS.eCache[i] = [1, Ei] # set valid #choose the alpha that gives the maximum delta E
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validEcacheList = nonzero(oS.eCache[:, 0].A)[0]
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if (len(validEcacheList)) > 1:
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for k in validEcacheList: # loop through valid Ecache values and find the one that maximizes delta E
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if k == i: continue # don't calc for i, waste of time
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Ek = calcEk(oS, k)
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deltaE = abs(Ei - Ek)
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if (deltaE > maxDeltaE):
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maxK = k;
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maxDeltaE = deltaE;
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Ej = Ek
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return maxK, Ej
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else: # in this case (first time around) we don't have any valid eCache values
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j = selectJrand(i, oS.m)
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Ej = calcEk(oS, j)
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return j, Ej
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def updateEkK(oS, k): # after any alpha has changed update the new value in the cache
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Ek = calcEk(oS, k)
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oS.eCache[k] = [1, Ek]
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def innerLK(i, oS):
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Ei = calcEk(oS, i)
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if ((oS.labelMat[i] * Ei < -oS.tol) and (oS.alphas[i] < oS.C)) or (
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(oS.labelMat[i] * Ei > oS.tol) and (oS.alphas[i] > 0)):
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j, Ej = selectJ(i, oS, Ei) # this has been changed from selectJrand
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alphaIold = oS.alphas[i].copy();
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alphaJold = oS.alphas[j].copy();
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if (oS.labelMat[i] != oS.labelMat[j]):
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L = max(0, oS.alphas[j] - oS.alphas[i])
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H = min(oS.C, oS.C + oS.alphas[j] - oS.alphas[i])
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else:
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L = max(0, oS.alphas[j] + oS.alphas[i] - oS.C)
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H = min(oS.C, oS.alphas[j] + oS.alphas[i])
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if L == H: print
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"L==H";
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return 0
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eta = 2.0 * oS.X[i, :] * oS.X[j, :].T - oS.X[i, :] * oS.X[i, :].T - oS.X[j, :] * oS.X[j, :].T
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if eta >= 0: print
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"eta>=0";
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return 0
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oS.alphas[j] -= oS.labelMat[j] * (Ei - Ej) / eta
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oS.alphas[j] = clipAlpha(oS.alphas[j], H, L)
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updateEk(oS, j) # added this for the Ecache
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if (abs(oS.alphas[j] - alphaJold) < 0.00001): print
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"j not moving enough";
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return 0
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oS.alphas[i] += oS.labelMat[j] * oS.labelMat[i] * (alphaJold - oS.alphas[j]) # update i by the same amount as j
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updateEk(oS, i) # added this for the Ecache #the update is in the oppostie direction
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b1 = oS.b - Ei - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.X[i, :] * oS.X[i, :].T - oS.labelMat[j] * (
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oS.alphas[j] - alphaJold) * oS.X[i, :] * oS.X[j, :].T
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b2 = oS.b - Ej - oS.labelMat[i] * (oS.alphas[i] - alphaIold) * oS.X[i, :] * oS.X[j, :].T - oS.labelMat[j] * (
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oS.alphas[j] - alphaJold) * oS.X[j, :] * oS.X[j, :].T
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if (0 < oS.alphas[i]) and (oS.C > oS.alphas[i]):
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oS.b = b1
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elif (0 < oS.alphas[j]) and (oS.C > oS.alphas[j]):
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oS.b = b2
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else:
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oS.b = (b1 + b2) / 2.0
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return 1
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else:
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return 0
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def smoPK(dataMatIn, classLabels, C, toler, maxIter): # full Platt SMO
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oS = optStruct(mat(dataMatIn), mat(classLabels).transpose(), C, toler)
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iter = 0
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entireSet = True;
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alphaPairsChanged = 0
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while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
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alphaPairsChanged = 0
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if entireSet: # go over all
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for i in range(oS.m):
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alphaPairsChanged += innerL(i, oS)
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print("fullSet, iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged))
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iter += 1
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else: # go over non-bound (railed) alphas
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nonBoundIs = nonzero((oS.alphas.A > 0) * (oS.alphas.A < C))[0]
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for i in nonBoundIs:
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alphaPairsChanged += innerL(i, oS)
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print("non-bound, iter: %d i:%d, pairs changed %d" % (iter, i, alphaPairsChanged))
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iter += 1
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if entireSet:
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entireSet = False # toggle entire set loop
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elif (alphaPairsChanged == 0):
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entireSet = True
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print("iteration number: %d" % iter)
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return oS.b, oS.alphas
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