def testDigits(kTrup=('rbf', 10)):
trainingDigits = 'F:\\panrui\\我的桌面\\learning file\\machinelearninginaction\\Ch06\\trainingDigits'
dataArr, labelArr = loadImages(trainingDigits)
b, alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, kTrup)
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, :], kTrup)
predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
if sign(predict) != sign(labelArr[i]):
errorCount += 1
print("the training error 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, :], kTrup)
predict = kernelEval.T * multiply(labelSV, alphas[svInd]) + b
if sign(predict) != sign(labelArr[i]):
errorCount += 1
print("the training error is: %f" % (float(errorCount) / m))
def kernelTrans(X, A, kTup):
m, n = shape(X)
K = mat(zeros((m, 1)))
if kTup[0] == 'lin': K = X * A.T
elif kTup[0] == 'rbf':
for j in range(m):
deltaRow = X[j, :] - A
K[j] = deltaRow * deltaRow.T
K = exp(K / (-1 * kTup[1]**2))
else:
raise NameError('that Kernel is not recognized')
return K
def haar_inverse(image, dim=2):
'''
Apply haar inverse transformation.
:param image: square matrix
:param dim: dimension
:return: None
'''
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = T.T * P.T * M.asmatrix(image[0:dim, 0:dim]) * P * T
if dim == M.shape(image)[0]:
return
haar_inverse(image, dim * 2)
def haar_inverse(image, dim=2):
'''
Apply haar inverse transformation.
:param image: square matrix
:param dim: dimension
:return: None
'''
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = T.T * P.T * M.asmatrix(image[0:dim, 0:dim]) * P * T
if dim == M.shape(image)[0]:
return
haar_inverse(image, dim * 2)
def haar_forward(image, dim=None, recursive=True):
'''
Apply haar transformation to image.
:param image: square matrix
:param dim: dimension
:param recursive: apply recursively
:return: None
'''
if dim is None:
dim = M.shape(image)[0]
if dim == 1: # base case
return
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = P * T * M.asmatrix(image[0:dim, 0:dim]) * T.T * P.T
if recursive:
haar_forward(image, dim / 2)
def haar_forward(image, dim=None, recursive=True):
'''
Apply haar transformation to image.
:param image: square matrix
:param dim: dimension
:param recursive: apply recursively
:return: None
'''
if dim is None:
dim = M.shape(image)[0]
if dim == 1: # base case
return
P = permutation_matrix(dim)
T = haar_matrix(dim)
image[0:dim, 0:dim] = P * T * M.asmatrix(image[0:dim, 0:dim]) * T.T * P.T
if recursive:
haar_forward(image, dim / 2)
def QuadProg(H, c, Ae, be, Ai, bi, x0):
epsilon = 1e-9
err = 1e-6
k = 0
x = x0
n = len(x)
kmax = 1e2
ne = len(be)
ni = len(bi)
index = mat.ones((ni, 1))
for i in range(0, ni):
if Ai[i, :] * x > bi[i] + epsilon:
index[i] = 0
while k <= kmax:
Aee = []
#if ne > 0:
# Aee = Ae
AeeList = []
if ne > 0:
AeeList.append(Ae)
for j in range(0, ni):
if index[j] > 0:
AeeList.append(Ai[j, :])
#Aee = mat.vstack((Aee, Ai[j,:]))
if len(AeeList) == 0:
Aee = []
else:
Aee = mat.vstack(AeeList)
m1, n1 = mat.shape(Aee)
gk = H * x + c
dk, lamk = qsubp(H, gk, Aee, mat.zeros((m1, 1)))
if np.linalg.norm(dk) <= err:
y = 0.0
if len(lamk) > ne:
jk = np.argmin(lamk[ne:len(lamk)])
y = lamk[jk]
if y >= 0:
exitflag = 0
else:
exitflag = 1
for i in range(0, ni):
if index[i] and (ne + sum(index[0:i])) == jk:
index[i] = 0
break
#k += 1
else:
exitflag = 1
alpha = 1.0
tm = 1.0
for i in range(0, ni):
if index[i] == 0 and Ai[i, :] * dk < 0:
tmm = (bi[i] - Ai[i, :] * x) / (Ai[i, :] * dk)
tm1 = abs(tmm[0, 0])
if tm1 < tm:
tm = tm1
ti = i
alpha = min(alpha, abs(tm))
x = x + alpha * dk
if tm < 1:
index[ti] = 1
if exitflag == 0:
break
k += 1
print k
return x
def QuadProg(H, c, Ae, be, Ai, bi, x0):
epsilon = 1e-9
err = 1e-6
k = 0
x = x0
n = len(x)
kmax = 1e2
ne = len(be)
ni = len(bi)
index = mat.ones((ni, 1))
for i in range(0, ni):
if Ai[i,:] * x > bi[i] + epsilon:
index[i] = 0
while k <= kmax:
Aee = []
#if ne > 0:
# Aee = Ae
AeeList = []
if ne > 0:
AeeList.append(Ae)
for j in range(0, ni):
if index[j] > 0:
AeeList.append(Ai[j, :])
#Aee = mat.vstack((Aee, Ai[j,:]))
if len(AeeList) == 0:
Aee = []
else:
Aee = mat.vstack(AeeList)
m1, n1 = mat.shape(Aee)
gk = H * x + c
dk, lamk = qsubp(H, gk, Aee, mat.zeros((m1, 1)))
if np.linalg.norm(dk) <= err:
y = 0.0
if len(lamk) > ne:
jk = np.argmin(lamk[ne:len(lamk)])
y = lamk[jk]
if y >= 0:
exitflag = 0
else:
exitflag = 1
for i in range(0, ni):
if index[i] and (ne + sum(index[0:i])) == jk:
index[i] = 0;
break;
#k += 1
else:
exitflag = 1
alpha = 1.0
tm = 1.0
for i in range(0, ni):
if index[i] == 0 and Ai[i, :] * dk < 0:
tmm = (bi[i] - Ai[i, :] * x) / (Ai[i, :] * dk)
tm1 = abs(tmm[0,0])
if tm1 < tm:
tm = tm1;
ti = i;
alpha = min(alpha, abs(tm))
x = x + alpha * dk
if tm < 1:
index[ti] = 1
if exitflag == 0:
break
k += 1
print k
return x
