TF/04_Support_Vector_Machines/06_Implementing_Multiclass_SVMs

06 Implementing Multiclass SVMs

Here, we implement a 1-vs-all voting method for a multiclass SVM. We attempt to separate the three Iris flower classes with TensorFlow.

# 06_multiclass_svm.py# Multi-class (Nonlinear) SVM Example#----------------------------------## This function wll illustrate how to# implement the gaussian kernel with# multiple classes on the iris dataset.## Gaussian Kernel:# K(x1, x2) = exp(-gamma * abs(x1 - x2)^2)## X : (Sepal Length, Petal Width)# Y: (I. setosa, I. virginica, I. versicolor) (3 classes)## Basic idea: introduce an extra dimension to do# one vs all classification.## The prediction of a point will be the category with# the largest margin or distance to boundary.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_vals1 = np.array([1 if y==0 else -1 for y in iris.target])y_vals2 = np.array([1 if y==1 else -1 for y in iris.target])y_vals3 = np.array([1 if y==2 else -1 for y in iris.target])y_vals = np.array([y_vals1, y_vals2, y_vals3])class1_x = [x[0] for i,x in enumerate(x_vals) if iris.target[i]==0]class1_y = [x[1] for i,x in enumerate(x_vals) if iris.target[i]==0]class2_x = [x[0] for i,x in enumerate(x_vals) if iris.target[i]==1]class2_y = [x[1] for i,x in enumerate(x_vals) if iris.target[i]==1]class3_x = [x[0] for i,x in enumerate(x_vals) if iris.target[i]==2]class3_y = [x[1] for i,x in enumerate(x_vals) if iris.target[i]==2]# Declare batch sizebatch_size = 50# Initialize placeholdersx_data = tf.placeholder(shape=[None, 2], dtype=tf.float32)y_target = tf.placeholder(shape=[3, None], dtype=tf.float32)prediction_grid = tf.placeholder(shape=[None, 2], dtype=tf.float32)# Create variables for svmb = tf.Variable(tf.random_normal(shape=[3,batch_size]))# Gaussian (RBF) kernelgamma = tf.constant(-10.0)dist = tf.reduce_sum(tf.square(x_data), 1)dist = tf.reshape(dist, [-1,1])sq_dists = tf.multiply(2., tf.matmul(x_data, tf.transpose(x_data)))my_kernel = tf.exp(tf.multiply(gamma, tf.abs(sq_dists)))# Declare function to do reshape/batch multiplicationdef reshape_matmul(mat):    v1 = tf.expand_dims(mat, 1)    v2 = tf.reshape(v1, [3, batch_size, 1])    return(tf.matmul(v2, v1))# Compute SVM Modelfirst_term = tf.reduce_sum(b)b_vec_cross = tf.matmul(tf.transpose(b), b)y_target_cross = reshape_matmul(y_target)second_term = tf.reduce_sum(tf.multiply(my_kernel, tf.multiply(b_vec_cross, y_target_cross)),[1,2])loss = tf.reduce_sum(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(y_target,b), pred_kernel)prediction = tf.arg_max(prediction_output-tf.expand_dims(tf.reduce_mean(prediction_output,1), 1), 0)accuracy = tf.reduce_mean(tf.cast(tf.equal(prediction, tf.argmax(y_target,0)), 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(100):    rand_index = np.random.choice(len(x_vals), size=batch_size)    rand_x = x_vals[rand_index]    rand_y = 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)%25==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='I. versicolor')plt.plot(class3_x, class3_y, 'gv', label='I. virginica')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 #25Loss = -321.294Step #50Loss = -658.794Step #75Loss = -996.294Step #100Loss = -1333.79