基于TensorFlow支持向量机

1、导入必要编程库

import matplotlib.pyplot as plt
import numpy as np
import tensorflow as tf
from sklearn import datasets

2、创建会话，生成模拟数据

sess = tf.Session()
(x_vals, y_vals) = datasets.make_circles(n_samples=500, 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]

3、生成批量大小，占位符等

batch_size = 250
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)
b = tf.Variable(tf.random_normal(shape = [1, batch_size]))

4、创建高斯核函数
高斯核函数：

k (| | x - x c | |) = e^{（ \frac{- | | x - x c | |^{2}}{(2 * σ)^{2}} ）}

$k(||x-xc||)=e^{（\frac{- ||x-xc||^2}{(2*σ)^2 }）}$

gamma = 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)))

5、声明支持向量机的对偶问题

model_output = tf.matmul(b,my_kernel)

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))

6、创建预测函数和准确度函数


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)))

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))

7、创建优化器函数


my_opt = tf.train.GradientDescentOptimizer(0.001)
train_step = my_opt.minimize(loss)
init = tf.global_variables_initializer()
sess.run(init)

8、开始迭代训练

loss_vec = []

batch_accuracy = []

for i in range(5000):
    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)%100==0:
        print('Step # ' + str(i+1))
        print('Loss = ' + str(temp_loss))

9、输出结果

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)

plt.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, 'rx',label='Class -1')
plt.legend(loc='lower right')
plt.ylim([-1.5,1.5])
plt.xlim([-1.5,1.5])
plt.show()

plt.plot(batch_accuracy,'k-',label='Accuracy')
plt.title('Batch Accuracy')
plt.xlabel('Generation')
plt.ylabel('Accuracy')

plt.legend(loc = 'Lower right')
plt.show()

plt.plot(loss_vec,'k-')
plt.title('Loss per Generation')
plt.xlabel('Generation')
plt.ylabel('Loss')

plt.show()

10、训练结果
这里写图片描述

基于TensorFlow支持向量机

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