SVM的實現原理

svm的**是實現原理

1）計算核函式

def calckernelvalue(matrix_x, sample_x, kerneloption)：
kerneltype = kerneloption[0]
numsamples = matrix_x.shape[0]
kernelvalue = mat(zeros((numsamples, 1)))
if kerneltype == 'linear':
kernelvalue = matrix_x * sample_x.t
elif kerneltype == 'rbf':
sigma = kerneloption[1]
if sigma == 0:
sigma = 1.0
for i in range(numsamples):
diff = matrix_x[i, :] - sample_x
kernelvalue[i] = exp(diff * diff.t / (-2.0 * sigma ** 2))
else:
raise nameerror('not support kernel type! you can use linear or rbf!')
return kernelvalue

2）選擇最大迭代次數aj

第一步：選擇aj

def selectalpha_j(svm, alpha_i, error_i):
svm.errorcache[alpha_i] = [1, error_i] # mark as valid(has been optimized)
candidatealphalist = nonzero(svm.errorcache[:, 0].a)[0] # mat.a return array
maxstep = 0;
alpha_j = 0;
error_j = 0
# find the alpha with max iterative step
if len(candidatealphalist) > 1:
for alpha_k in candidatealphalist:
if alpha_k == alpha_i:
continue
error_k = mysvm.calcerror(svm, alpha_k)
if abs(error_k - error_i) > maxstep:
maxstep = abs(error_k - error_i)
alpha_j = alpha_k
error_j = error_k
# if came in this loop first time, we select alpha j randomly
else:
alpha_j = alpha_i
while alpha_j == alpha_i:
alpha_j = int(random.uniform(0, svm.numsamples))
error_j = mysvm.calcerror(svm, alpha_j)
return alpha_j, error_j

第二步：計算上下界

alpha_j, error_j = mysvm.selectalpha_j(svm, alpha_i, error_i)
alpha_i_old = svm.alphas[alpha_i].copy()
alpha_j_old = svm.alphas[alpha_j].copy()

eta = 2.0 * svm.kernelmat[alpha_i, alpha_j] - svm.kernelmat[alpha_i, alpha_i] 
- svm.kernelmat[alpha_j, alpha_j]
if eta >= 0:
return 0

第四步：更新aj

svm.alphas[alpha_j] -= svm.train_y[alpha_j] * (error_i - error_j) / eta

第五步：確保aj在上下界範圍以內

if svm.alphas[alpha_j] > h:
svm.alphas[alpha_j] = h
if svm.alphas[alpha_j] < l:
svm.alphas[alpha_j] = l

第六步：根據更新後的aj更新ai

svm.alphas[alpha_i] += svm.train_y[alpha_i] * svm.train_y[alpha_j] \
* (alpha_j_old - svm.alphas[alpha_j])

第七步：更新閾值b

b1 = svm.b - error_i - svm.train_y[alpha_i] * (svm.alphas[alpha_i] - alpha_i_old) \
* svm.kernelmat[alpha_i, alpha_i] \
- svm.train_y[alpha_j] * (svm.alphas[alpha_j] - alpha_j_old) \
* svm.kernelmat[alpha_i, alpha_j]
b2 = svm.b - error_j - svm.train_y[alpha_i] * (svm.alphas[alpha_i] - alpha_i_old) \
* svm.kernelmat[alpha_i, alpha_j] \
- svm.train_y[alpha_j] * (svm.alphas[alpha_j] - alpha_j_old) \
* svm.kernelmat[alpha_j, alpha_j]
if (0 < svm.alphas[alpha_i]) and (svm.alphas[alpha_i] < svm.c):
svm.b = b1
elif (0 < svm.alphas[alpha_j]) and (svm.alphas[alpha_j] < svm.c):
svm.b = b2
else:
svm.b = (b1 + b2) / 2.0

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