TensorFlow实现非线性支持向量机的实现方法

这里将加载iris数据集，创建一个山鸢尾花（I.setosa）的分类器。

# 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 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)] # 加载iris数据集，抽取花萼长度和花瓣宽度，分割每类的x_vals值和y_vals值 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 size # 声明批量大小（偏向于更大批量大小） batch_size = 150 # Initialize placeholders x_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 svm b = tf.Variable(tf.random_normal(shape=[1,batch_size])) # Gaussian (RBF) kernel # 声明批量大小（偏向于更大批量大小） gamma = 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 Model first_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 kernel # 创建一个预测核函数 rA = 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))) # 声明一个准确度函数，其为正确分类的数据点的百分比 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 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 = [] 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 in # 为了绘制决策边界（Decision Boundary），我们创建一个数据点（x，y）的网格，评估预测函数 x_min, x_max = x_vals[:, 0].min() - 1, x_vals[:, 0].max() + 1 y_min, y_max = x_vals[:, 1].min() - 1, x_vals[:, 1].max() + 1 xx, 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 grid plt.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 accuracy plt.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 time plt.plot(loss_vec, 'k-') plt.title('Loss per Generation') plt.xlabel('Generation') plt.ylabel('Loss') plt.show()

输出：

Step #75
Loss = -110.332
Step #150
Loss = -222.832
Step #225
Loss = -335.332
Step #300
Loss = -447.832

四种不同的gamma值（1，10，25，100）:

 

 

 

 

不同gamma值的山鸢尾花（I.setosa）的分类器结果图，采用高斯核函数的SVM。

gamma值越大，每个数据点对分类边界的影响就越大。

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非线性 方法 支持向量机 tensorflow 线性