iris二分类
# Linear Support Vector Machine: Soft Margin# ----------------------------------## This function shows how to use TensorFlow to# create a soft margin SVM## We will use the iris data, specifically:# x1 = Sepal Length# x2 = Petal Width# Class 1 : I. setosa# Class -1: not I. setosa## We know here that x and y are linearly seperable# for I. setosa classification.import matplotlib.pyplot as pltimport numpy as npimport tensorflow as tffrom sklearn import datasetsfrom tensorflow.python.framework import opsops.reset_default_graph()# Set random seedsnp.random.seed(7)tf.set_random_seed(7)# Create graphsess = 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 setstrain_indices = np.random.choice(len(x_vals), round(len(x_vals)*0.9), 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 sizebatch_size = 135# Initialize placeholdersx_data = tf.placeholder(shape=[None, 2], dtype=tf.float32)y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)# Create variables for linear regressionA = tf.Variable(tf.random_normal(shape=[2, 1]))b = tf.Variable(tf.random_normal(shape=[1, 1]))# Declare model operationsmodel_output = tf.subtract(tf.matmul(x_data, A), b)# Declare vector L2 'norm' function squaredl2_norm = tf.reduce_sum(tf.square(A))# Declare loss function# Loss = max(0, 1-pred*actual) + alpha * L2_norm(A)^2# L2 regularization parameter, alphaalpha = tf.constant([0.01])# Margin term in lossclassification_term = tf.reduce_mean(tf.maximum(0., tf.subtract(1., tf.multiply(model_output, y_target))))# Put terms togetherloss = tf.add(classification_term, tf.multiply(alpha, l2_norm))# Declare prediction functionprediction = tf.sign(model_output)accuracy = tf.reduce_mean(tf.cast(tf.equal(prediction, y_target), tf.float32)# Declare optimizermy_opt = tf.train.GradientDescentOptimizer(0.01)train_step = my_opt.minimize(loss)# Initialize variablesinit = tf.global_variables_initializer()sess.run(init)# Training looploss_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 #{} A = {}, b = {}'.format( str(i+1), str(sess.run(A)), str(sess.run(b)) )) print('Loss = ' + str(temp_loss))# Extract coefficients[[a1], [a2]] = sess.run(A)[[b]] = sess.run(b)slope = -a2/a1y_intercept = b/a1# Extract x1 and x2 valsx1_vals = [d[1] for d in x_vals]# Get best fit linebest_fit = []for i in x1_vals: best_fit.append(slope*i+y_intercept)# Separate I. setosasetosa_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 lineplt.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 accuraciesplt.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 timeplt.plot(loss_vec, 'k-')plt.title('Loss per Generation')plt.xlabel('Generation')plt.ylabel('Loss')plt.show()
下面的例子数据集可能更好看；
# SVM Regression#----------------------------------## This function shows how to use TensorFlow to# solve support vector regression. We are going# to find the line that has the maximum margin# which INCLUDES as many points as possible## We will use the iris data, specifically:# y = Sepal Length# x = Pedal Widthimport matplotlib.pyplot as pltimport numpy as npimport tensorflow as tffrom sklearn import datasetsfrom tensorflow.python.framework import opsops.reset_default_graph()# Create graphsess = tf.Session()# Load the data# iris.data = [(Sepal Length, Sepal Width, Petal Length, Petal Width)]iris = datasets.load_iris()x_vals = np.array([x[3] for x in iris.data])y_vals = np.array([y[0] for y in iris.data])# Split data into train/test setstrain_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 sizebatch_size = 50# Initialize placeholdersx_data = tf.placeholder(shape=[None, 1], dtype=tf.float32)y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)# Create variables for linear regressionA = tf.Variable(tf.random_normal(shape=[1,1]))b = tf.Variable(tf.random_normal(shape=[1,1]))# Declare model operationsmodel_output = tf.add(tf.matmul(x_data, A), b)# Declare loss function# = max(0, abs(target - predicted) + epsilon)# 1/2 margin width parameter = epsilonepsilon = tf.constant([0.5])# Margin term in lossloss = tf.reduce_mean(tf.maximum(0., tf.subtract(tf.abs(tf.subtract(model_output, y_target)), epsilon)))# Declare optimizermy_opt = tf.train.GradientDescentOptimizer(0.075)train_step = my_opt.minimize(loss)# Initialize variablesinit = tf.global_variables_initializer()sess.run(init)# Training looptrain_loss = []test_loss = []for i in range(200): rand_index = np.random.choice(len(x_vals_train), size=batch_size) rand_x = np.transpose([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_train_loss = sess.run(loss, feed_dict={x_data: np.transpose([x_vals_train]), y_target: np.transpose([y_vals_train])}) train_loss.append(temp_train_loss) temp_test_loss = sess.run(loss, feed_dict={x_data: np.transpose([x_vals_test]), y_target: np.transpose([y_vals_test])}) test_loss.append(temp_test_loss) if (i+1)%50==0: print('-----------') print('Generation: ' + str(i+1)) print('A = ' + str(sess.run(A)) + ' b = ' + str(sess.run(b))) print('Train Loss = ' + str(temp_train_loss)) print('Test Loss = ' + str(temp_test_loss))# Extract Coefficients[[slope]] = sess.run(A)[[y_intercept]] = sess.run(b)[width] = sess.run(epsilon)# Get best fit linebest_fit = []best_fit_upper = []best_fit_lower = []for i in x_vals: best_fit.append(slope*i+y_intercept) best_fit_upper.append(slope*i+y_intercept+width) best_fit_lower.append(slope*i+y_intercept-width)# Plot fit with dataplt.plot(x_vals, y_vals, 'o', label='Data Points')plt.plot(x_vals, best_fit, 'r-', label='SVM Regression Line', linewidth=3)plt.plot(x_vals, best_fit_upper, 'r--', linewidth=2)plt.plot(x_vals, best_fit_lower, 'r--', linewidth=2)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 loss over timeplt.plot(train_loss, 'k-', label='Train Set Loss')plt.plot(test_loss, 'r--', label='Test Set Loss')plt.title('L2 Loss per Generation')plt.xlabel('Generation')plt.ylabel('L2 Loss')plt.legend(loc='upper right')plt.show()
事实上，高斯核函数的应用也可以自定义许多核函数：
# Illustration of Various Kernels#----------------------------------## This function wll illustrate how to# implement various kernels in TensorFlow.## Linear Kernel:# K(x1, x2) = t(x1) * x2## Gaussian Kernel (RBF):# K(x1, x2) = exp(-gamma * abs(x1 - x2)^2)import matplotlib.pyplot as pltimport numpy as npimport tensorflow as tffrom sklearn import datasetsfrom tensorflow.python.framework import opsops.reset_default_graph()# Create graphsess = tf.Session()# Generate non-lnear data(x_vals, y_vals) = datasets.make_circles(n_samples=350, factor=.5, noise=.1)y_vals = np.array([1 if y==1 else -1 for y in y_vals])class1_x = [x[0] for i,x in enumerate(x_vals) if y_vals[i]==1]class1_y = [x[1] for i,x in enumerate(x_vals) if y_vals[i]==1]class2__x = [x[0] for i,x in enumerate(x_vals) if y_vals[i]==-1]class2__y = [x[1] for i,x in enumerate(x_vals) if y_vals[i]==-1]# Declare batch sizebatch_size = 350# Initialize placeholdersx_data = tf.placeholder(shape=[None, 2], dtype=tf.float32)y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)prediction_grid = tf.placeholder(shape=[None, 2], dtype=tf.float32)# Create variables for svmb = tf.Variable(tf.random_normal(shape=[1,batch_size]))# Apply kernel# Linear Kernel# my_kernel = tf.matmul(x_data, tf.transpose(x_data))# Gaussian (RBF) kernelgamma = tf.constant(-50.0)dist = tf.reduce_sum(tf.square(x_data), 1)dist = tf.reshape(dist, [-1,1])sq_dists = tf.add(tf.subtract(dist, tf.multiply(2., tf.matmul(x_data, tf.transpose(x_data)))), tf.transpose(dist))my_kernel = tf.exp(tf.multiply(gamma, tf.abs(sq_dists)))# Compute SVM Modelfirst_term = tf.reduce_sum(b)b_vec_cross = tf.matmul(tf.transpose(b), b)y_target_cross = tf.matmul(y_target, tf.transpose(y_target))second_term = tf.reduce_sum(tf.multiply(my_kernel, tf.multiply(b_vec_cross, y_target_cross)))loss = tf.negative(tf.subtract(first_term, second_term))# Create Prediction Kernel# Linear prediction kernel# my_kernel = tf.matmul(x_data, tf.transpose(prediction_grid))# Gaussian (RBF) prediction kernelrA = tf.reshape(tf.reduce_sum(tf.square(x_data), 1),[-1,1])rB = tf.reshape(tf.reduce_sum(tf.square(prediction_grid), 1)，[-1，1]pred_sq_dist = tf.add(tf.subtract(rA, tf.multiply(2., tf.matmul(x_data, tf.transpose(prediction_grid)))), tf.transpose(rB))pred_kernel = tf.exp(tf.multiply(gamma, tf.abs(pred_sq_dist)))prediction_output = tf.matmul(tf.multiply(tf.transpose(y_target),b), pred_kernel)prediction = tf.sign(prediction_output-tf.reduce_mean(prediction_output))accuracy = tf.reduce_mean(tf.cast(tf.equal(tf.squeeze(prediction), tf.squeeze(y_target)), tf.float32)# Declare optimizermy_opt = tf.train.GradientDescentOptimizer(0.002)train_step = my_opt.minimize(loss)# Initialize variablesinit = tf.global_variables_initializer()sess.run(init)# Training looploss_vec = []batch_accuracy = []for i in range(1000): rand_index = np.random.choice(len(x_vals), size=batch_size) rand_x = x_vals[rand_index] rand_y = np.transpose([y_vals[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) acc_temp = sess.run(accuracy, feed_dict={x_data: rand_x, y_target: rand_y, prediction_grid:rand_x}) batch_accuracy.append(acc_temp) if (i+1)%250==0: print('Step #' + str(i+1)) print('Loss = ' + str(temp_loss))# Create a mesh to plot points inx_min, x_max = x_vals[:, 0].min() - 1, x_vals[:, 0].max() + 1y_min, y_max = x_vals[:, 1].min() - 1, x_vals[:, 1].max() + 1xx, yy = np.meshgrid(np.arange(x_min, x_max, 0.02), np.arange(y_min, y_max, 0.02))grid_points = np.c_[xx.ravel(), yy.ravel()][grid_predictions] = sess.run(prediction, feed_dict={x_data: rand_x, y_target: rand_y, prediction_grid: grid_points})grid_predictions = grid_predictions.reshape(xx.shape)# Plot points and gridplt.contourf(xx, yy, grid_predictions, cmap=plt.cm.Paired, alpha=0.8)plt.plot(class1_x, class1_y, 'ro', label='Class 1')plt.plot(class2___x, class2__y, 'kx', label='Class -1')plt.title('Gaussian SVM Results')plt.xlabel('x')plt.ylabel('y')plt.legend(loc='lower right')plt.ylim([-1.5, 1.5])plt.xlim([-1.5, 1.5])plt.show()# Plot batch accuracyplt.plot(batch_accuracy, 'k-', label='Accuracy')plt.title('Batch Accuracy')plt.xlabel('Generation')plt.ylabel('Accuracy')plt.legend(loc='lower right')plt.show()# Plot loss over timeplt.plot(loss_vec, 'k-')plt.title('Loss per Generation')plt.xlabel('Generation')plt.ylabel('Loss')plt.show()# Evaluate on new/unseen data points# New data points:new_points = np.array([(-0.75, -0.75), (-0.5, -0.5), (-0.25, -0.25), (0.25, 0.25), (0.5, 0.5), (0.75, 0.75)])[evaluations] = sess.run(prediction, feed_dict={x_data: x_vals, y_target: np.transpose([y_vals]), prediction_grid: new_points})for ix, p in enumerate(new_points): print('{} : class={}'.format(p, evaluations[ix]))
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