TensorFlow实现非线性支持向量机的实现方法
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2023-10-18 21:09:08
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
#------------------...
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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