你要的答案或许都在这里：小鹏的博客目录
我想说：
其实很多事情一定要找好自己的节奏，因为你会发现你不会的东西太多了，千万不要被带跑了。
上两节：MachineLN之SVM（1）、MachineLN之SVM（2），讲述了SVM的原理，今天看一下带详细注释的源码 和 tensorflow使用梯度下降求解svm参数：切记好代码都是敲出来的，并且越敲越有感觉，本想着还是截图， 但是代码太多了
from numpy import *
from time import sleep
# 依旧是数据的准备
def loadDataSet(fileName):
# 定义保存样本和标签的列表;
dataMat = []; labelMat = [a]
# 打开数据文件
fr = open(fileName)
# 读取文件中的每一行;
for line in fr.readlines():
# 将每行的数据通过制表符分开;
lineArr = line.strip().split('\t')
# 前两个为样本数据数据，第二个为标签数据;
dataMat.append([float(lineArr[0]), float(lineArr[1])])
labelMat.append(float(lineArr[2]))
# 返回样本和标签，用于SVM的训练;
return dataMat,labelMat
# 用于产生一个随机数，用于下面随机获取一个样本;
def selectJrand(i,m):
j=i #we want to select any J not equal to i
while (j==i):
j = int(random.uniform(0,m))
return j
# 相当于给定alpha一个范围，大于最大值的话，赋值为最大值，小于最小值的话，就赋值最小值;
def clipAlpha(aj,H,L):
if aj > H:
aj = H
if L > aj:
aj = L
return aj
# 简化版的smo算法求alpha和b;
# 下面是smo算法的流程;
# 此简化版的smo是严格按照上一节MachineLN之SVM（2）的手撕smo来的；
def smoSimple(dataMatIn, classLabels, C, toler, maxIter):
# 将样本集转化为矩阵格式， 将样本的标签也转化为矩阵格式和，用于后面的矩阵运算， 主要两个地方用到：预测和eta。
dataMatrix = mat(dataMatIn); labelMat = mat(classLabels).transpose()
# 初始化偏置，然后获取矩阵的行数和列数， 行数用来输出初始化下面的alpha.
b = 0; m,n = shape(dataMatrix)
# 初始化alphas为为m行1列；
alphas = mat(zeros((m,1)))
iter = 0
# 定义迭代次数
while (iter < maxIter):
alphaPairsChanged = 0
# 遍历每个样本;
for i in range(m):
# 计算第i个样本的预测标签; 用于计算差值；
fXi = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[i,:].T)) + b
# 计算两个的差值用于 KKT 条件的判断
Ei = fXi - float(labelMat[i])#if checks if an example violates KKT conditions
# 正间隔 和 负间隔 都会被测试; 并且还要保证 alpha的值在 [0, C]之间
if ((labelMat[i]*Ei < -toler) and (alphas[i] < C)) or ((labelMat[i]*Ei > toler) and (alphas[i] > 0)):
# 从 i到m中随机选择一个样本
j = selectJrand(i,m)
# 计算此样本的预测值
fXj = float(multiply(alphas,labelMat).T*(dataMatrix*dataMatrix[j,:].T)) + b
# 预测值和真实值的差值： 用于后面计算alpha.
Ej = fXj - float(labelMat[j])
# 用于保存未更新的alpha，方便b的计算;
alphaIold = alphas[i].copy(); alphaJold = alphas[j].copy();
# 计算不同的情况下 aphpa 的最小值和最大值， 这里可以参考手撕smo;
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
# 下面就是计算alpha2 和 进行剪枝后，求alpha1;
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
# 更新参数b1， b2， 和手撕smo算法流程一样;
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
# 根据参数b1， b2得到b;
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
# 下面就是核函数：线性核函数 和 rbf核函数
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 # 线性核
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)) # rbf核
else: raise NameError('Houston We Have a Problem -- \
That Kernel is not recognized')
return K
# 利用完整的 Platt SMO算法加速运算;
# 与简化版相比：实现alpha的更改和代数运算的优化环节一摸一样，在优化过程中唯一不同的就是选择alpha的方式。
# 用于设置模型中的数据和参数： 训练样本、标签、学习率、KKT条件的参数设置值、alpha、b、核函数的参数；
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))) # 用于误差缓存
self.K = mat(zeros((self.m,self.m)))
for i in range(self.m):
self.K[:,i] = kernelTrans(self.X, self.X[i,:], kTup)
# 计算预测值和真实值的标签的差值;
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
# 在选择第一个alpha值后，算法会通过内循环来选择第二个alpha值，在优化过程中，会通过最大步长的方式来获得第二个alpha值
# 选择合适的第二个样本; 计算Ej
def selectJ(i, oS, Ei):
maxK = -1; maxDeltaE = 0; Ej = 0
# 将其放在Ei缓存区。
oS.eCache[i] = [1,Ei] #set valid #choose the alpha that gives the maximum delta E
# 返回的是非零E值所对应的alpha值，而不是E本身，程序会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；
# else中， 在第一次的循环的话， 那么就随机选择一个alpha值。
validEcacheList = nonzero(oS.eCache[:,0].A)[0]
if (len(validEcacheList)) > 1:
for k in validEcacheList:
if k == i: continue
Ek = calcEk(oS, k)
deltaE = abs(Ei - Ek)
if (deltaE > maxDeltaE):
maxK = k; maxDeltaE = deltaE; Ej = Ek
return maxK, Ej
else:
j = selectJrand(i, oS.m)
Ej = calcEk(oS, j)
return j, Ej
# 更新选取新样本后的E值
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]
# 下面的算法流程和简化版的smo流程差不多
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
# Platt AMO算法
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
# 通过计算的alpha计算权重w值
def calcWs(alphas,dataArr,classLabels):
X = mat(dataArr); labelMat = mat(classLabels).transpose()
m,n = shape(X)
w = zeros((n,1))
# 计算 w
for i in range(m):
w += multiply(alphas[i]*labelMat[i],X[i,:].T)
return w
# 使用rbf核的svm，进行测试
def testRbf(k1=1.3):
dataArr,labelArr = loadDataSet('testSetRBF.txt')
# 通过Platt AMO算法计算alpha和b的值
b,alphas = smoP(dataArr, labelArr, 200, 0.0001, 10000, ('rbf', k1)) #C=200 important
#
datMat=mat(dataArr); labelMat = mat(labelArr).transpose()
# 构建支持向量矩阵， 选择 0<alpha<C
svInd=nonzero(alphas.A>0)[0]
# 仅选支持向量用于kernel相乘
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
# 下面是计算在训练集的错误率
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)
# 下面是求在测试集的错误率
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)
# 下面是手写体识别的svm测试
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)
tensorflow梯度下降法求解模型参数：
# SVM梯度下降进参数求解
import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from sklearn import datasets
from tensorflow.python.framework import ops
ops.reset_default_graph()
# Create graph
sess = tf.Session()
# Load the data
# iris.data = [(Sepal Length, Sepal Width, Petal Length, Petal Width)]
iris = datasets.load_iris()
x_vals = np.array([[x[0], x[3]] for x in iris.data])
y_vals = np.array([1 if y==0 else -1 for y in iris.target])
# Split data into train/test sets
train_indices = np.random.choice(len(x_vals), round(len(x_vals)*0.8), replace=False)
test_indices = np.array(list(set(range(len(x_vals))) - set(train_indices)))
x_vals_train = x_vals[train_indices]
x_vals_test = x_vals[test_indices]
y_vals_train = y_vals[train_indices]
y_vals_test = y_vals[test_indices]
# Declare batch size
batch_size = 100
# Initialize placeholders
x_data = tf.placeholder(shape=[None, 2], dtype=tf.float32)
y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)
# Create variables for linear regression
A = tf.Variable(tf.random_normal(shape=[2,1]))
b = tf.Variable(tf.random_normal(shape=[1,1]))
# Declare model operations
model_output = tf.subtract(tf.matmul(x_data, A), b)
# 定义 hinge loss function
# Declare vector L2 'norm' function squared
l2_norm = tf.reduce_sum(tf.square(A))
# Declare loss function
# Loss = max(0, 1-pred*actual) + alpha * L2_norm(A)^2
# L2 regularization parameter, alpha
alpha = tf.constant([0.01])
# Margin term in loss
classification_term = tf.reduce_mean(tf.maximum(0., tf.subtract(1., tf.multiply(model_output, y_target))))
# Put terms together
loss = tf.add(classification_term, tf.multiply(alpha, l2_norm))
# Declare prediction function
prediction = tf.sign(model_output)
accuracy = tf.reduce_mean(tf.cast(tf.equal(prediction, y_target), tf.float32))
# Declare optimizer
my_opt = tf.train.GradientDescentOptimizer(0.01)
train_step = my_opt.minimize(loss)
# Initialize variables
init = tf.global_variables_initializer()
sess.run(init)
# Training loop
loss_vec = []
train_accuracy = []
test_accuracy = []
for i in range(500):
rand_index = np.random.choice(len(x_vals_train), size=batch_size)
rand_x = x_vals_train[rand_index]
rand_y = np.transpose([y_vals_train[rand_index]])
sess.run(train_step, feed_dict={x_data: rand_x, y_target: rand_y})
temp_loss = sess.run(loss, feed_dict={x_data: rand_x, y_target: rand_y})
loss_vec.append(temp_loss)
train_acc_temp = sess.run(accuracy, feed_dict={x_data: x_vals_train, y_target: np.transpose([y_vals_train])})
train_accuracy.append(train_acc_temp)
test_acc_temp = sess.run(accuracy, feed_dict={x_data: x_vals_test, y_target: np.transpose([y_vals_test])})
test_accuracy.append(test_acc_temp)
if (i+1)%100==0:
print('Step #' + str(i+1) + ' A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b)))
print('Loss = ' + str(temp_loss))
# Extract coefficients
[[a1], [a2]] = sess.run(A)
[[b]] = sess.run(b)
slope = -a2/a1
y_intercept = b/a1
# Extract x1 and x2 vals
x1_vals = [d[1] for d in x_vals]
# Get best fit line
best_fit = []
for i in x1_vals:
best_fit.append(slope*i+y_intercept)
# Separate I. setosa
setosa_x = [d[1] for i,d in enumerate(x_vals) if y_vals[i]==1]
setosa_y = [d[0] for i,d in enumerate(x_vals) if y_vals[i]==1]
not_setosa_x = [d[1] for i,d in enumerate(x_vals) if y_vals[i]==-1]
not_setosa_y = [d[0] for i,d in enumerate(x_vals) if y_vals[i]==-1]
# Plot data and line
plt.plot(setosa_x, setosa_y, 'o', label='I. setosa')
plt.plot(not_setosa_x, not_setosa_y, 'x', label='Non-setosa')
plt.plot(x1_vals, best_fit, 'r-', label='Linear Separator', linewidth=3)
plt.ylim([0, 10])
plt.legend(loc='lower right')
plt.title('Sepal Length vs Pedal Width')
plt.xlabel('Pedal Width')
plt.ylabel('Sepal Length')
plt.show()
# Plot train/test accuracies
plt.plot(train_accuracy, 'k-', label='Training Accuracy')
plt.plot(test_accuracy, 'r--', label='Test Accuracy')
plt.title('Train and Test Set Accuracies')
plt.xlabel('Generation')
plt.ylabel('Accuracy')
plt.legend(loc='lower right')
plt.show()
# Plot loss over time
plt.plot(loss_vec, 'k-')
plt.title('Loss per Generation')
plt.xlabel('Generation')
plt.ylabel('Loss')
plt.show()
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