支持向量机算法

简介: 支持向量机算法

谷歌笔记本(可选)

from google.colab import drive
drive.mount("/content/drive")
Mounted at /content/drive

SMO高效优化算法

import random
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, labelMat
def selectJrand(i, m):
  j=i
  while(j==i):
    j = int(random.uniform(0, m))
  return j
def clipAlpha(aj, H, L):
  if aj > H:
    aj = H
  if L > aj:
    aj = L
  return aj
dataArr, labelArr = loadDataSet('/content/drive/MyDrive/Colab Notebooks/MachineLearning/《机器学习实战》/支持向量机/支持向量机/testSet.txt')
labelArr
[-1.0,
 -1.0,
 1.0,
 -1.0,
 1.0,
 1.0,
 1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 1.0,
 -1.0,
 1.0,
 1.0,
 -1.0,
 1.0,
 -1.0,
 -1.0,
 -1.0,
 1.0,
 -1.0,
 -1.0,
 1.0,
 1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 -1.0,
 1.0,
 -1.0,
 -1.0,
 1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 -1.0,
 1.0,
 1.0,
 -1.0,
 -1.0,
 1.0,
 1.0,
 -1.0,
 1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 1.0,
 -1.0,
 1.0,
 -1.0,
 -1.0,
 1.0,
 1.0,
 1.0,
 -1.0,
 1.0,
 1.0,
 -1.0,
 -1.0,
 1.0,
 -1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 1.0,
 -1.0,
 1.0,
 1.0,
 1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0,
 -1.0]
from numpy import *
def 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 checks if an example violates KKT conditions
            if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):
                j = selectJrand(i,m)
                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])#update i by the same amount as j
                                                                        #the update is in the oppostie direction
                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

这是一个简化版的SMO(Sequential Minimal Optimization)算法,用于支持向量机的训练。


输入参数:


  • dataMatIn: 输入数据的特征矩阵
  • classLabels: 输入数据的类别标签
  • C: 软间隔参数,在优化目标函数时对误分类样本的惩罚程度
  • toler: 容错率,用于控制支持向量的选择
  • maxIter: 最大迭代次数

输出结果:

  • b: SMO算法中的常数项
  • alphas: 支持向量的拉格朗日乘子

算法主要步骤:

  1. 初始化一些参数,包括数据矩阵的大小、拉格朗日乘子矩阵等。
  2. 在最大迭代次数内进行迭代,直到所有的乘子不再更新或达到最大迭代次数。
  3. 针对每个样本,计算样本的预测值和误差,并检查是否违反了KKT条件(KKT条件是支持向量机优化问题的充要条件之一)。
  4. 如果违反了KKT条件,选择一个样本作为更新的对象,并计算该样本的预测值和误差。
  5. 根据样本的类别标签,计算L和H的值,用于限制拉格朗日乘子的取值范围。
  6. 计算alpha的更新量eta,并检查eta是否大于等于0,如果是,则继续选择新的样本进行更新。
  7. 更新alpha的值,同时限制其在L和H之间的范围。
  8. 检查alpha的更新幅度是否足够大,如果不够大,则继续选择新的样本进行更新。
  9. 更新常数项b的值,根据更新前后的alpha值和对应的样本信息。
  10. 记录更新的乘子数量,并根据乘子数量是否发生变化来判断是否继续迭代。
  11. 返回最终的常数项和乘子矩阵。

注:其中的函数selectJrand()用于随机选择乘子的索引,clipAlpha()用于限制乘子的取值范围。

b, alphas = smoSimple(dataArr, labelArr, 0.6, 0.001, 40)
<ipython-input-10-609e212d7149>:9: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
  fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
<ipython-input-10-609e212d7149>:10: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
  Ei = fXi - float(labelMat[i])#if checks if an example violates KKT conditions
<ipython-input-10-609e212d7149>:13: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
  fXj = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + b
<ipython-input-10-609e212d7149>:14: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
  Ej = fXj - float(labelMat[j])


iter: 0 i:0, pairs changed 1
L==H
j not moving enough
L==H
L==H
L==H
L==H
L==H
……
j not moving enough
j not moving enough
iteration number: 40
b
matrix([[-3.82396091]])
alphas[alphas>0]
matrix([[0.09439001, 0.26843195, 0.0348491 , 0.32797286]])
shape(alphas[alphas>0])
(1, 4)
for i in range(100):
  if alphas[i] > 0:
    print(dataArr[i], labelArr[i])
[4.658191, 3.507396] -1.0
[3.457096, -0.082216] -1.0
[5.286862, -2.358286] 1.0
[6.080573, 0.418886] 1.0
import matplotlib.pyplot as plt
dataArr, labelArr = loadDataSet('/content/drive/MyDrive/Colab Notebooks/MachineLearning/《机器学习实战》/支持向量机/支持向量机/testSet.txt')
x = array(dataArr)[:, 0]
y = array(dataArr)[:, 1]
fig = plt.figure()
plt.scatter(x, y)
for i in range(100):
  if alphas[i] > 0:
    plt.scatter(dataArr[i][0], dataArr[i][1], color='red', s=20)
plt.show()

def kernelTrans(X, A, kTup): #calc the kernel or transform data to a higher dimensional space
    m,n = shape(X)
    K = mat(zeros((m,1)))
    if kTup[0]=='lin': K = X * A.T   #linear kernel
    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)) #divide in NumPy is element-wise not matrix like Matlab
    else: raise NameError('Houston We Have a Problem -- \
    That Kernel is not recognized')
    return K

该函数是用于计算核函数或者将数据转换到更高维空间的函数。函数的输入包括数据集X、一个参考数据集A和一个核函数类型kTup。


首先,函数获取输入数据集的行和列数,并创建一个全零矩阵K,维度为m行1列。


然后,根据核函数类型选择不同的计算方法。如果核函数类型为’lin’,则采用线性核函数的计算方式,即将输入数据集X与参考数据集A的转置矩阵相乘。


如果核函数类型为’rbf’,则采用径向基函数(RBF)核函数的计算方式。首先遍历输入数据集X的每一行,计算每一行与参考数据集A的欧氏距离的平方,并存储在K矩阵中。然后,使用指数函数将K矩阵中的每个元素除以核函数参数的平方,并取负数。


最后,如果核函数类型不是’lin’也不是’rbf’,则报错提示核函数类型不被识别。

最后,函数返回计算得到的K矩阵。

class optStruct:
    def __init__(self,dataMatIn, classLabels, C, toler, kTup):  # Initialize the structure with the parameters
        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))) #first column is valid flag
        self.K = mat(zeros((self.m,self.m)))
        for i in range(self.m):
            self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup)

这段代码是定义了一个名为optStruct的类,该类包含了一些变量和方法。


类的初始化函数__init__接受5个参数:dataMatIn、classLabels、C、toler和kTup。


  • dataMatIn是一个表示数据矩阵的输入
  • classLabels是一个表示类别标签的输入
  • C是一个常数,用于调整目标函数中的惩罚项
  • toler是一个容错率,用于控制在数值计算中的误差
  • kTup是一个元组,表示核函数的类型和参数

初始化函数中,将输入的参数赋值给类的成员变量。


其中,self.alphas是一个m行1列的矩阵,用于存储拉格朗日乘子

self.b是一个常数,用于计算分类器的偏置

self.eCache是一个m行2列的矩阵,用于存储计算过程中的误差缓存

self.K是一个m行m列的矩阵,用于存储样本间的核函数计算结果然后,使用一个循环来计算核函数矩阵self.K的值。循环从0到self.m-1,每次取出self.X的第i行作为参数,调用kernelTrans函数计算核函数的结果,并将结果赋值给self.K的第i列。

def calcEk(oS, k):
    fXk = float(multiply(oS.alphas,oS.labelMat).T*oS.K[:,k] + oS.b)
    Ek = fXk - float(oS.labelMat[k])
    return Ek
def selectJ(i, oS, Ei):         #this is the second choice -heurstic, and calcs Ej
    maxK = -1; maxDeltaE = 0; Ej = 0
    oS.eCache[i] = [1,Ei]  #set valid #choose the alpha that gives the maximum delta E
    validEcacheList = nonzero(oS.eCache[:,0].A)[0]
    if (len(validEcacheList)) > 1:
        for k in validEcacheList:   #loop through valid Ecache values and find the one that maximizes delta E
            if k == i: continue #don't calc for i, waste of time
            Ek = calcEk(oS, k)
            deltaE = abs(Ei - Ek)
            if (deltaE > maxDeltaE):
                maxK = k; maxDeltaE = deltaE; Ej = Ek
        return maxK, Ej
    else:   #in this case (first time around) we don't have any valid eCache values
        j = selectJrand(i, oS.m)
        Ej = calcEk(oS, j)
    return j, Ej
def updateEk(oS, k):#after any alpha has changed update the new value in the cache
    Ek = calcEk(oS, k)
    oS.eCache[k] = [1,Ek]
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) #this has been changed from selectJrand
        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.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) #added this for the Ecache
        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) #added this for the Ecache                    #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 smoP(dataMatIn, classLabels, C, toler, maxIter,kTup=('lin', 0)):    #full Platt SMO
    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:   #go over all
            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:#go over non-bound (railed) alphas
            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 #toggle entire set loop
        elif (alphaPairsChanged == 0): entireSet = True
        print("iteration number: %d" % iter)
    return oS.b,oS.alphas
import matplotlib.pyplot as plt
dataArr, labelArr = loadDataSet('/content/drive/MyDrive/Colab Notebooks/MachineLearning/《机器学习实战》/支持向量机/支持向量机/testSet.txt')
b, alphas = smoP(dataArr, labelArr, 0.6, 0.001, 40)
x = array(dataArr)[:, 0]
y = array(dataArr)[:, 1]
fig = plt.figure()
plt.scatter(x, y)
for i in range(100):
  if alphas[i] > 0:
    plt.scatter(dataArr[i][0], dataArr[i][1], color='red', s=20)
plt.show()
<ipython-input-48-c1e41c4ea928>:2: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
  fXk = float(multiply(oS.alphas,oS.labelMat).T*oS.K[:,k] + oS.b)
<ipython-input-48-c1e41c4ea928>:3: DeprecationWarning: Conversion of an array with ndim > 0 to a scalar is deprecated, and will error in future. Ensure you extract a single element from your array before performing this operation. (Deprecated NumPy 1.25.)
  Ek = fXk - float(oS.labelMat[k])


fullSet, iter: 0 i:0, pairs changed 1
fullSet, iter: 0 i:1, pairs changed 1
fullSet, iter: 0 i:2, pairs changed 2
fullSet, iter: 0 i:3, pairs changed 2
fullSet, iter: 0 i:4, pairs changed 3
fullSet, iter: 0 i:5, pairs changed 4
fullSet, iter: 0 i:6, pairs changed 4
fullSet, iter: 0 i:7, pairs changed 4
j not moving enough
fullSet, iter: 0 i:8, pairs changed 4
fullSet, iter: 0 i:9, pairs changed 4
j not moving enough
fullSet, iter: 0 i:10, pairs changed 4
fullSet, iter: 0 i:11, pairs changed 4
fullSet, iter: 0 i:12, pairs changed 4
fullSet, iter: 0 i:13, pairs changed 4
fullSet, iter: 0 i:14, pairs changed 4
fullSet, iter: 0 i:15, pairs changed 4
fullSet, iter: 0 i:16, pairs changed 4
fullSet, iter: 0 i:17, pairs changed 5
fullSet, iter: 0 i:18, pairs changed 6
fullSet, iter: 0 i:19, pairs changed 6
j not moving enough
fullSet, iter: 0 i:20, pairs changed 6
j not moving enough
fullSet, iter: 0 i:21, pairs changed 6
fullSet, iter: 0 i:22, pairs changed 6
fullSet, iter: 0 i:23, pairs changed 7
fullSet, iter: 0 i:24, pairs changed 7
j not moving enough
fullSet, iter: 0 i:25, pairs changed 7
L==H
fullSet, iter: 0 i:26, pairs changed 7
fullSet, iter: 0 i:27, pairs changed 7
fullSet, iter: 0 i:28, pairs changed 7
L==H
fullSet, iter: 0 i:29, pairs changed 7
fullSet, iter: 0 i:30, pairs changed 7
fullSet, iter: 0 i:31, pairs changed 7
fullSet, iter: 0 i:32, pairs changed 7
fullSet, iter: 0 i:33, pairs changed 7
fullSet, iter: 0 i:34, pairs changed 7
fullSet, iter: 0 i:35, pairs changed 7
fullSet, iter: 0 i:36, pairs changed 7
fullSet, iter: 0 i:37, pairs changed 7
fullSet, iter: 0 i:38, pairs changed 7
j not moving enough
fullSet, iter: 0 i:39, pairs changed 7
fullSet, iter: 0 i:40, pairs changed 7
fullSet, iter: 0 i:41, pairs changed 7
fullSet, iter: 0 i:42, pairs changed 7
fullSet, iter: 0 i:43, pairs changed 7
fullSet, iter: 0 i:44, pairs changed 7
fullSet, iter: 0 i:45, pairs changed 7
L==H
fullSet, iter: 0 i:46, pairs changed 7
fullSet, iter: 0 i:47, pairs changed 7
fullSet, iter: 0 i:48, pairs changed 7
fullSet, iter: 0 i:49, pairs changed 7
fullSet, iter: 0 i:50, pairs changed 7
fullSet, iter: 0 i:51, pairs changed 7
L==H
fullSet, iter: 0 i:52, pairs changed 7
fullSet, iter: 0 i:53, pairs changed 7
L==H
fullSet, iter: 0 i:54, pairs changed 7
L==H
fullSet, iter: 0 i:55, pairs changed 7
fullSet, iter: 0 i:56, pairs changed 7
L==H
fullSet, iter: 0 i:57, pairs changed 7
fullSet, iter: 0 i:58, pairs changed 7
fullSet, iter: 0 i:59, pairs changed 7
fullSet, iter: 0 i:60, pairs changed 7
fullSet, iter: 0 i:61, pairs changed 7
L==H
fullSet, iter: 0 i:62, pairs changed 7
fullSet, iter: 0 i:63, pairs changed 7
fullSet, iter: 0 i:64, pairs changed 7
fullSet, iter: 0 i:65, pairs changed 7
fullSet, iter: 0 i:66, pairs changed 7
fullSet, iter: 0 i:67, pairs changed 7
fullSet, iter: 0 i:68, pairs changed 7
L==H
fullSet, iter: 0 i:69, pairs changed 7
fullSet, iter: 0 i:70, pairs changed 7
fullSet, iter: 0 i:71, pairs changed 7
fullSet, iter: 0 i:72, pairs changed 7
fullSet, iter: 0 i:73, pairs changed 7
fullSet, iter: 0 i:74, pairs changed 7
fullSet, iter: 0 i:75, pairs changed 7
fullSet, iter: 0 i:76, pairs changed 7
fullSet, iter: 0 i:77, pairs changed 7
fullSet, iter: 0 i:78, pairs changed 7
L==H
fullSet, iter: 0 i:79, pairs changed 7
fullSet, iter: 0 i:80, pairs changed 7
fullSet, iter: 0 i:81, pairs changed 7
L==H
fullSet, iter: 0 i:82, pairs changed 7
fullSet, iter: 0 i:83, pairs changed 7
fullSet, iter: 0 i:84, pairs changed 7
fullSet, iter: 0 i:85, pairs changed 7
fullSet, iter: 0 i:86, pairs changed 7
fullSet, iter: 0 i:87, pairs changed 7
fullSet, iter: 0 i:88, pairs changed 7
fullSet, iter: 0 i:89, pairs changed 7
fullSet, iter: 0 i:90, pairs changed 7
fullSet, iter: 0 i:91, pairs changed 7
fullSet, iter: 0 i:92, pairs changed 7
fullSet, iter: 0 i:93, pairs changed 7
fullSet, iter: 0 i:94, pairs changed 7
fullSet, iter: 0 i:95, pairs changed 7
fullSet, iter: 0 i:96, pairs changed 7
fullSet, iter: 0 i:97, pairs changed 7
fullSet, iter: 0 i:98, pairs changed 7
fullSet, iter: 0 i:99, pairs changed 7
iteration number: 1
j not moving enough
non-bound, iter: 1 i:0, pairs changed 0
non-bound, iter: 1 i:4, pairs changed 1
non-bound, iter: 1 i:5, pairs changed 2
j not moving enough
non-bound, iter: 1 i:17, pairs changed 2
non-bound, iter: 1 i:18, pairs changed 3
non-bound, iter: 1 i:23, pairs changed 4
iteration number: 2
j not moving enough
non-bound, iter: 2 i:0, pairs changed 0
j not moving enough
non-bound, iter: 2 i:5, pairs changed 0
j not moving enough
non-bound, iter: 2 i:17, pairs changed 0
non-bound, iter: 2 i:23, pairs changed 0
j not moving enough
non-bound, iter: 2 i:52, pairs changed 0
non-bound, iter: 2 i:55, pairs changed 0
iteration number: 3
j not moving enough
fullSet, iter: 3 i:0, pairs changed 0
fullSet, iter: 3 i:1, pairs changed 0
fullSet, iter: 3 i:2, pairs changed 0
fullSet, iter: 3 i:3, pairs changed 0
fullSet, iter: 3 i:4, pairs changed 0
j not moving enough
fullSet, iter: 3 i:5, pairs changed 0
fullSet, iter: 3 i:6, pairs changed 0
fullSet, iter: 3 i:7, pairs changed 0
fullSet, iter: 3 i:8, pairs changed 0
fullSet, iter: 3 i:9, pairs changed 0
fullSet, iter: 3 i:10, pairs changed 0
fullSet, iter: 3 i:11, pairs changed 0
fullSet, iter: 3 i:12, pairs changed 0
fullSet, iter: 3 i:13, pairs changed 0
fullSet, iter: 3 i:14, pairs changed 0
fullSet, iter: 3 i:15, pairs changed 0
fullSet, iter: 3 i:16, pairs changed 0
j not moving enough
fullSet, iter: 3 i:17, pairs changed 0
fullSet, iter: 3 i:18, pairs changed 0
fullSet, iter: 3 i:19, pairs changed 0
fullSet, iter: 3 i:20, pairs changed 0
fullSet, iter: 3 i:21, pairs changed 0
fullSet, iter: 3 i:22, pairs changed 0
fullSet, iter: 3 i:23, pairs changed 0
fullSet, iter: 3 i:24, pairs changed 0
fullSet, iter: 3 i:25, pairs changed 0
fullSet, iter: 3 i:26, pairs changed 0
fullSet, iter: 3 i:27, pairs changed 0
fullSet, iter: 3 i:28, pairs changed 0
j not moving enough
fullSet, iter: 3 i:29, pairs changed 0
fullSet, iter: 3 i:30, pairs changed 0
fullSet, iter: 3 i:31, pairs changed 0
fullSet, iter: 3 i:32, pairs changed 0
fullSet, iter: 3 i:33, pairs changed 0
fullSet, iter: 3 i:34, pairs changed 0
fullSet, iter: 3 i:35, pairs changed 0
fullSet, iter: 3 i:36, pairs changed 0
fullSet, iter: 3 i:37, pairs changed 0
fullSet, iter: 3 i:38, pairs changed 0
fullSet, iter: 3 i:39, pairs changed 0
fullSet, iter: 3 i:40, pairs changed 0
fullSet, iter: 3 i:41, pairs changed 0
fullSet, iter: 3 i:42, pairs changed 0
fullSet, iter: 3 i:43, pairs changed 0
fullSet, iter: 3 i:44, pairs changed 0
fullSet, iter: 3 i:45, pairs changed 0
fullSet, iter: 3 i:46, pairs changed 0
fullSet, iter: 3 i:47, pairs changed 0
fullSet, iter: 3 i:48, pairs changed 0
fullSet, iter: 3 i:49, pairs changed 0
fullSet, iter: 3 i:50, pairs changed 0
fullSet, iter: 3 i:51, pairs changed 0
j not moving enough
fullSet, iter: 3 i:52, pairs changed 0
fullSet, iter: 3 i:53, pairs changed 0
L==H
fullSet, iter: 3 i:54, pairs changed 0
fullSet, iter: 3 i:55, pairs changed 0
fullSet, iter: 3 i:56, pairs changed 0
fullSet, iter: 3 i:57, pairs changed 0
fullSet, iter: 3 i:58, pairs changed 0
fullSet, iter: 3 i:59, pairs changed 0
fullSet, iter: 3 i:60, pairs changed 0
fullSet, iter: 3 i:61, pairs changed 0
fullSet, iter: 3 i:62, pairs changed 0
fullSet, iter: 3 i:63, pairs changed 0
fullSet, iter: 3 i:64, pairs changed 0
fullSet, iter: 3 i:65, pairs changed 0
fullSet, iter: 3 i:66, pairs changed 0
fullSet, iter: 3 i:67, pairs changed 0
fullSet, iter: 3 i:68, pairs changed 0
fullSet, iter: 3 i:69, pairs changed 0
fullSet, iter: 3 i:70, pairs changed 0
fullSet, iter: 3 i:71, pairs changed 0
fullSet, iter: 3 i:72, pairs changed 0
fullSet, iter: 3 i:73, pairs changed 0
fullSet, iter: 3 i:74, pairs changed 0
fullSet, iter: 3 i:75, pairs changed 0
fullSet, iter: 3 i:76, pairs changed 0
fullSet, iter: 3 i:77, pairs changed 0
fullSet, iter: 3 i:78, pairs changed 0
fullSet, iter: 3 i:79, pairs changed 0
fullSet, iter: 3 i:80, pairs changed 0
fullSet, iter: 3 i:81, pairs changed 0
fullSet, iter: 3 i:82, pairs changed 0
fullSet, iter: 3 i:83, pairs changed 0
fullSet, iter: 3 i:84, pairs changed 0
fullSet, iter: 3 i:85, pairs changed 0
fullSet, iter: 3 i:86, pairs changed 0
fullSet, iter: 3 i:87, pairs changed 0
fullSet, iter: 3 i:88, pairs changed 0
fullSet, iter: 3 i:89, pairs changed 0
fullSet, iter: 3 i:90, pairs changed 0
fullSet, iter: 3 i:91, pairs changed 0
fullSet, iter: 3 i:92, pairs changed 0
fullSet, iter: 3 i:93, pairs changed 0
fullSet, iter: 3 i:94, pairs changed 0
fullSet, iter: 3 i:95, pairs changed 0
fullSet, iter: 3 i:96, pairs changed 0
fullSet, iter: 3 i:97, pairs changed 0
fullSet, iter: 3 i:98, pairs changed 0
fullSet, iter: 3 i:99, pairs changed 0
iteration number: 4

def 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
def testRbf(k1=1.3):
    dataArr,labelArr = loadDataSet('testSetRBF.txt')
    b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) #C=200 important
    datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
    svInd=nonzero(alphas.A>0)[0]
    sVs=datMat[svInd] #get matrix of only support vectors
    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))
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 returnVect
def loadImages(dirName):
    from os import listdir
    hwLabels = []
    trainingFileList = listdir(dirName)           #load the training set
    m = len(trainingFileList)
    trainingMat = zeros((m,1024))
    for i in range(m):
        fileNameStr = trainingFileList[i]
        fileStr = fileNameStr.split('.')[0]     #take off .txt
        classNumStr = int(fileStr.split('_')[0])
        if classNumStr == 9: hwLabels.append(-1)
        else: hwLabels.append(1)
        trainingMat[i,:] = img2vector('%s/%s' % (dirName, fileNameStr))
    return trainingMat, hwLabels
def 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 Vectors" % 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))
class optStructK:
    def __init__(self,dataMatIn, classLabels, C, toler):  # Initialize the structure with the parameters
        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))) #first column is valid flag

def calcEkK(oS, k):
    fXk = float(multiply(oS.alphas,oS.labelMat).T*(oS.X*oS.X[k,:].T)) + oS.b
    Ek = fXk - float(oS.labelMat[k])
    return Ek

def selectJK(i, oS, Ei):         #this is the second choice -heurstic, and calcs Ej
    maxK = -1; maxDeltaE = 0; Ej = 0
    oS.eCache[i] = [1,Ei]  #set valid #choose the alpha that gives the maximum delta E
    validEcacheList = nonzero(oS.eCache[:,0].A)[0]
    if (len(validEcacheList)) > 1:
        for k in validEcacheList:   #loop through valid Ecache values and find the one that maximizes delta E
            if k == i: continue #don't calc for i, waste of time
            Ek = calcEk(oS, k)
            deltaE = abs(Ei - Ek)
            if (deltaE > maxDeltaE):
                maxK = k; maxDeltaE = deltaE; Ej = Ek
        return maxK, Ej
    else:   #in this case (first time around) we don't have any valid eCache values
        j = selectJrand(i, oS.m)
        Ej = calcEk(oS, j)
    return j, Ej

def updateEkK(oS, k):#after any alpha has changed update the new value in the cache
    Ek = calcEk(oS, k)
    oS.eCache[k] = [1,Ek]

def innerLK(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) #this has been changed from selectJrand
        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
        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) #added this for the Ecache
        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) #added this for the Ecache                    #the update is in the oppostie direction
        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
        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 smoPK(dataMatIn, classLabels, C, toler, maxIter):    #full Platt SMO
    oS = optStruct(mat(dataMatIn),mat(classLabels).transpose(),C,toler)
    iter = 0
    entireSet = True; alphaPairsChanged = 0
    while (iter < maxIter) and ((alphaPairsChanged > 0) or (entireSet)):
        alphaPairsChanged = 0
        if entireSet:   #go over all
            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:#go over non-bound (railed) alphas
            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 #toggle entire set loop
        elif (alphaPairsChanged == 0): entireSet = True
        print("iteration number: %d" % iter)
    return oS.b,oS.alphas
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