机器学习-21:MachineLN之SVM源码
2018-02-01 09:24
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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
tensorflow梯度下降法求解模型参数:
推荐阅读:
1. 机器学习-1:MachineLN之三要素
2. 机器学习-2:MachineLN之模型评估
3. 机器学习-3:MachineLN之dl
4. 机器学习-4:DeepLN之CNN解析
5. 机器学习-5:DeepLN之CNN权重更新(笔记)
6. 机器学习-6:DeepLN之CNN源码
7. 机器学习-7:MachineLN之激活函数
8. 机器学习-8:DeepLN之BN
9. 机器学习-9:MachineLN之数据归一化
10. 机器学习-10:MachineLN之样本不均衡
11. 机器学习-11:MachineLN之过拟合
12. 机器学习-12:MachineLN之优化算法
13. 机器学习-13:MachineLN之kNN
14. 机器学习-14:MachineLN之kNN源码
15. 机器学习-15:MachineLN之感知机
16. 机器学习-16:MachineLN之感知机源码
17. 机器学习-17:MachineLN之逻辑回归
18. 机器学习-18:MachineLN之逻辑回归源码
19. 机器学习-19:MachineLN之SVM(1)
20. 机器学习-20:MachineLN之SVM(2)
21. 机器学习-21:MachineLN之SVM源码
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()
推荐阅读:
1. 机器学习-1:MachineLN之三要素
2. 机器学习-2:MachineLN之模型评估
3. 机器学习-3:MachineLN之dl
4. 机器学习-4:DeepLN之CNN解析
5. 机器学习-5:DeepLN之CNN权重更新(笔记)
6. 机器学习-6:DeepLN之CNN源码
7. 机器学习-7:MachineLN之激活函数
8. 机器学习-8:DeepLN之BN
9. 机器学习-9:MachineLN之数据归一化
10. 机器学习-10:MachineLN之样本不均衡
11. 机器学习-11:MachineLN之过拟合
12. 机器学习-12:MachineLN之优化算法
13. 机器学习-13:MachineLN之kNN
14. 机器学习-14:MachineLN之kNN源码
15. 机器学习-15:MachineLN之感知机
16. 机器学习-16:MachineLN之感知机源码
17. 机器学习-17:MachineLN之逻辑回归
18. 机器学习-18:MachineLN之逻辑回归源码
19. 机器学习-19:MachineLN之SVM(1)
20. 机器学习-20:MachineLN之SVM(2)
21. 机器学习-21:MachineLN之SVM源码
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