基于TensorFlow的非线性向量机

1、导入必要的编程库；

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

2、加载数据集，分割数据；

sess = tf.Session()
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]

3、声明批量大小、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、声明高斯核函数核和模型；

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)))

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))

5、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)))

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))

6、声明优化函数、初始化变量；

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

batch_accuracy = []

7、开始迭代训练

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

8、创建一个数据点（x，y)的网格，评估预测预测函数。

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)

9、绘制决策边界

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, 'rx',label='Non setosa')
plt.legend(loc='lower right')
plt.ylim([-0.5,3])
plt.xlim([3.5,8.5])
plt.show()

运行结果：