TF/04_Support_Vector_Machines/05_Implementing_Nonlinear_SVMs

05 Implementing NonLinear SVMs

Here we show how to use the prior Gaussian RBF kernel to predict I.setosa from the Iris dataset.

# 05_nonlinear_svm.py# Nonlinear SVM Example#----------------------------------## This function wll illustrate how to# implement the gaussian kernel on# the iris dataset.## Gaussian Kernel:# 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()# 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])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 = 150# 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]))# Gaussian (RBF) kernelgamma = tf.constant(-25.0)sq_dists = tf.multiply(2., tf.matmul(x_data, tf.transpose(x_data)))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))# 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(0.01)train_step = my_opt.minimize(loss)# Initialize variablesinit = tf.global_variables_initializer()sess.run(init)# Training looploss_vec = []batch_accuracy = []for i in range(300):    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)%75==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='I. setosa')plt.plot(class2_x, class2_y, 'kx', label='Non setosa')plt.title('Gaussian SVM Results on Iris Data')plt.xlabel('Pedal Length')plt.ylabel('Sepal Width')plt.legend(loc='lower right')plt.ylim([-0.5, 3.0])plt.xlim([3.5, 8.5])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()

Step #75Loss = -111.979Step #150Loss = -224.479Step #225Loss = -336.979Step #300Loss = -449.479