# 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)
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


• 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

• b: SMO算法中的常数项
• alphas: 支持向量的拉格朗日乘子

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。

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
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

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)

• 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

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
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):
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))
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):
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)):
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))
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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