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更新SVM画图的分类颜色
This commit is contained in:
jiangzhonglian
@@ -39,14 +39,43 @@ class optStruct:
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# 误差缓存，第一列给出的是eCache是否有效的标志位，第二列给出的是实际的E值。
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self.eCache = mat(zeros((self.m, 2)))
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# m行m列的矩阵
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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 loadDataSet(fileName):
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def kernelTrans(X, A, kTup): # calc the kernel or transform data to a higher dimensional space
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"""
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对文件进行逐行解析，从而得到第行的类标签和整个数据矩阵
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核转换函数
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Args:
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X dataMatIn数据集
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A dataMatIn数据集的第i行的数据
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kTup 核函数的信息
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Returns:
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"""
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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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# linear kernel: m*n * n*1 = m*1
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K = X * A.T
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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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def loadDataSet(fileName):
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"""loadDataSet（对文件进行逐行解析，从而得到第行的类标签和整个数据矩阵）
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Args:
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fileName 文件名
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Returns:
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@@ -63,6 +92,186 @@ def loadDataSet(fileName):
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return dataMat, labelMat
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def calcEk(oS, k):
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"""calcEk（计算误差E值并返回）
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该过程在完整版的SMO算法中陪出现次数较多，因此将其单独作为一个方法
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Args:
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oS optStruct对象
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k 具体的某一行
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Returns:
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"""
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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 selectJrand(i, m):
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"""
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随机选择一个整数
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Args:
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i 第一个alpha的下标
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m 所有alpha的数目
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Returns:
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j 返回一个不为i的随机数，在0~m之间的整数值
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"""
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j = i
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while j == i:
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j = int(random.uniform(0, m))
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return j
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def selectJ(i, oS, Ei): # this is the second choice -heurstic, and calcs Ej
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"""selectJ（）
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内循环的启发式方法。
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选择第二个(内循环)alpha的alpha值
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这里的目标是选择合适的第二个alpha值以保证每次优化中采用最大步长。
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该函数的误差与第一个alpha值Ei和下标i有关。
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Args:
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i 具体的第i一行
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oS optStruct对象
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Ei 预测结果与真实结果比对，计算误差Ei
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Returns:
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j 随机选出的第j一行
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Ej 预测结果与真实结果比对，计算误差Ej
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"""
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maxK = -1
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maxDeltaE = 0
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Ej = 0
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# # 首先将输入值Ei在缓存中设置成为有效的。这里的有效意味着它已经计算好了。
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oS.eCache[i] = [1, Ei]
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# print 'oS.eCache[%s]=%s' % (i, oS.eCache[i])
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# print 'oS.eCache[:, 0].A=%s' % oS.eCache[:, 0].A.T
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# """
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# # 返回非0的：行列值
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# nonzero(oS.eCache[:, 0].A)= (
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# 行： array([ 0, 2, 4, 5, 8, 10, 17, 18, 20, 21, 23, 25, 26, 29, 30, 39, 46,52, 54, 55, 62, 69, 70, 76, 79, 82, 94, 97]),
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# 列： array([0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0,0, 0, 0, 0, 0])
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# )
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# """
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# print 'nonzero(oS.eCache[:, 0].A)=', nonzero(oS.eCache[:, 0].A)
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# # 取行的list
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# print 'nonzero(oS.eCache[:, 0].A)[0]=', nonzero(oS.eCache[:, 0].A)[0]
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# 非零E值的行的list列表，所对应的alpha值
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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: # 在所有的值上进行循环，并选择其中使得改变最大的那个值
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if k == i:
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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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# 选择具有最大步长的j
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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: # 如果是第一次循环，则随机选择一个alpha值
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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):
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"""
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计算误差值并存入缓存中。
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在对alpha值进行优化之后会用到这个值。
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Args:
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oS optStruct对象
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k:
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Returns:
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"""
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Ek = calcEk(oS, k)
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oS.eCache[k] = [1, Ek]
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def clipAlpha(aj, H, L):
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"""clipAlpha(调整aj的值，使aj处于 L<=aj<=H)
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Args:
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aj 目标值
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H 最大值
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L 最小值
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Returns:
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aj 目标值
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"""
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if aj > H:
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aj = H
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if L > aj:
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aj = L
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return aj
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def innerL(i, oS):
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"""
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内循环代码
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Args:
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i 具体的某一行
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oS optStruct对象
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Returns:
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"""
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# 预测结果与真实结果比对，计算误差Ei
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Ei = calcEk(oS, i)
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# 约束条件 (KKT条件是解决最优化问题的时用到的一种方法。我们这里提到的最优化问题通常是指对于给定的某一函数，求其在指定作用域上的全局最小值。)
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# 0<=alphas[i]<=C，但由于0和C是边界值，我们无法进行优化，因为需要增加一个alphas和降低一个alphas。
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# 表示发生错误的概率：labelMat[i]*Ei 如果超出了 toler， 才需要优化。至于正负号，我们考虑绝对值就对了。
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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)):
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# 选择最大的误差对应的j进行优化。效果更明显
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j, Ej = selectJ(i, oS, Ei)
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alphaIold = oS.alphas[i].copy()
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alphaJold = oS.alphas[j].copy()
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# L和H用于将alphas[j]调整到0-C之间。如果L==H，就不做任何改变，直接return 0
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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:
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print("L==H")
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return 0
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# eta是alphas[j]的最优修改量，如果eta==0，需要退出for循环的当前迭代过程
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# 如果ETA为0，那么计算新的alphas[j]就比较麻烦了, 为什么呢？ 因为2个值一样。
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# 2ab <= a^2 + b^2
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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:
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print("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) # 更新误差缓存
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if (abs(oS.alphas[j] - alphaJold) < 0.00001):
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print("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) # 更新误差缓存 #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)):
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"""
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完整SMO算法外循环，与smoSimple有些类似，但这里的循环退出条件更多一些
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@@ -79,10 +288,14 @@ def smoP(dataMatIn, classLabels, C, toler, maxIter, kTup=('lin', 0)):
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b 模型的常量值
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alphas 拉格朗日乘子
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"""
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# 创建一个 optStruct 对象
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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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# 循环遍历：
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while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
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alphaPairsChanged = 0
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if entireSet: # 在数据集上遍历所有可能的alpha
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@@ -124,7 +337,7 @@ def calcWs(alphas, dataArr, classLabels):
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return w
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def plotfig_SVM(xMat, yMat, ws, b, alphas):
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def plotfig_SVM(xArr, yArr, ws, b, alphas):
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"""
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参考地址：
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http://blog.csdn.net/maoersong/article/details/24315633
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@@ -132,8 +345,8 @@ def plotfig_SVM(xMat, yMat, ws, b, alphas):
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http://blog.csdn.net/kkxgx/article/details/6951959
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"""
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xMat = mat(xMat)
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yMat = mat(yMat)
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xMat = mat(xArr)
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yMat = mat(yArr)
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# b原来是矩阵，先转为数组类型后其数组大小为（1,1），所以后面加[0]，变为(1,)
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b = array(b)[0]
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@@ -149,8 +362,9 @@ def plotfig_SVM(xMat, yMat, ws, b, alphas):
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# 根据x.w + b = 0 得到，其式子展开为w0.x1 + w1.x2 + b = 0, x2就是y值
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y = (-b-ws[0, 0]*x)/ws[1, 0]
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ax.plot(x, y)
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for i in range(len(yMat)):
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if yMat[i, 0] > 0:
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for i in range(shape(yMat[0, :])[1]):
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if yMat[0, i] > 0:
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ax.plot(xMat[i, 0], xMat[i, 1], 'cx')
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else:
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ax.plot(xMat[i, 0], xMat[i, 1], 'kp')
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@@ -168,7 +382,7 @@ if __name__ == "__main__":
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# print labelArr
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# b是常量值， alphas是拉格朗日乘子
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b, alphas = smop(dataArr, labelArr, 0.6, 0.001, 40)
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b, alphas = smoP(dataArr, labelArr, 0.6, 0.001, 40)
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print '/n/n/n'
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print 'b=', b
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print 'alphas[alphas>0]=', alphas[alphas > 0]
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@@ -182,149 +396,32 @@ if __name__ == "__main__":
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def kernelTrans(X, A, kTup): # calc the kernel or transform data to a higher dimensional space
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"""
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核转换函数
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Args:
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X:
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A:
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kTup: 核函数的信息
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Returns:
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"""
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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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def calcEk(oS, k):
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"""
|
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计算E值并返回
|
||||
该过程在完整版的SMO算法中陪出现次数较多，因此将其单独作为一个方法
|
||||
Args:
|
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oS:
|
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k:
|
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|
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Returns:
|
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"""
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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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"""
|
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内循环的启发式方法。
|
||||
选择第二个(内循环)alpha的alpha值
|
||||
这里的目标是选择合适的第二个alpha值以保证每次优化中采用最大步长。
|
||||
该函数的误差与第一个alpha值Ei和下标i有关。
|
||||
Args:
|
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i:
|
||||
oS:
|
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Ei:
|
||||
|
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Returns:
|
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"""
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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] # 首先将输入值Ei在缓存中设置成为有效的。这里的有效意味着它已经计算好了。
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validEcacheList = nonzero(oS.eCache[:, 0].A)[0] # 非零E值所对应的alpha值
|
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if (len(validEcacheList)) > 1:
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for k in validEcacheList: # 在所有的值上进行循环，并选择其中使得改变最大的那个值
|
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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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# 选择具有最大步长的j
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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: # 如果是第一次循环，则随机选择一个alpha值
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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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"""
|
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计算误差值并存入缓存中。
|
||||
在对alpha值进行优化之后会用到这个值。
|
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Args:
|
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oS:
|
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k:
|
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Returns:
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"""
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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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"""
|
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内循环代码
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Args:
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i:
|
||||
oS:
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||||
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Returns:
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"""
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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]):
|
||||
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.K[i, j] - oS.K[i, i] - oS.K[j, j] # changed for kernel
|
||||
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) # 更新误差缓存
|
||||
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]) # update i by the same amount as j
|
||||
updateEk(oS, i) # 更新误差缓存 #the update is in the oppostie direction
|
||||
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
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
def testRbf(k1=1.3):
|
||||
@@ -435,6 +532,9 @@ def calcEkK(oS, k):
|
||||
return Ek
|
||||
|
||||
|
||||
|
||||
|
||||
|
||||
def selectJK(i, oS, Ei): # this is the second choice -heurstic, and calcs Ej
|
||||
maxK = -1
|
||||
maxDeltaE = 0
|
||||
|
||||
@@ -209,8 +209,9 @@ def plotfig_SVM(xMat, yMat, ws, b, alphas):
|
||||
# 根据x.w + b = 0 得到，其式子展开为w0.x1 + w1.x2 + b = 0, x2就是y值
|
||||
y = (-b-ws[0, 0]*x)/ws[1, 0]
|
||||
ax.plot(x, y)
|
||||
for i in range(len(yMat)):
|
||||
if yMat[i, 0] > 0:
|
||||
|
||||
for i in range(shape(yMat[0, :])[1]):
|
||||
if yMat[0, i] > 0:
|
||||
ax.plot(xMat[i, 0], xMat[i, 1], 'cx')
|
||||
else:
|
||||
ax.plot(xMat[i, 0], xMat[i, 1], 'kp')
|
||||
|
||||
Reference in New Issue
Block a user