机器学习之SVM原理与案例

定义：
支持向量机SVM（Support vector machine）是一种二值分类器方法,其基本是思想是：找到一个能够将两类分开的线性可分的直线（或者超平面）。实际上有许多条直线（或超平面）可以将两类目标分开来，我们要找的其实是这些直线（或超平面）中分割两类目标时，有最大距离的直线（或超平面）。我们称这样的直线或超平面为最佳线性分类器。如下图：

先看分类效果：

源码如下：

#引入库import matplotlib.pyplot as pltimport numpy as npimport tensorflow as tffrom sklearn import datasetsfrom tensorflow.python.framework import ops#创建图sess = tf.Session()#加载数据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])#分割数据集，80%的数据作为训练集用来训练，剩下20%的数据作为测试集用来做测试train_indices = np.random.choice(len(x_vals),                                 round(len(x_vals)*0.8),                                 replace=False)test_indices = np.array(list(set(range(len(x_vals))) - set(train_indices)))x_vals_train = x_vals[train_indices]x_vals_test = x_vals[test_indices]y_vals_train = y_vals[train_indices]y_vals_test = y_vals[test_indices]

# 声明批量大小batch_size = 100# 初始化占位符x_data = tf.placeholder(shape=[None, 2], dtype=tf.float32)y_target = tf.placeholder(shape=[None, 1], dtype=tf.float32)# 创建变量A = tf.Variable(tf.random_normal(shape=[2, 1]))b = tf.Variable(tf.random_normal(shape=[1, 1]))# 构建模型model_output = tf.subtract(tf.matmul(x_data, A), b)# 采用L2正则式l2_norm = tf.reduce_sum(tf.square(A))# 声明alpha参数alpha = tf.constant([0.01])term1=tf.subtract(1., tf.multiply(model_output, y_target))classification_term = tf.reduce_mean(tf.maximum(0., term1))# 定义损失函数loss = tf.add(classification_term, tf.multiply(alpha, l2_norm))# 声明预测函数和准确度函数prediction = tf.sign(model_output)accuracy = tf.reduce_mean(tf.cast(tf.equal(prediction, y_target), tf.float32))# 声明优化器my_opt = tf.train.GradientDescentOptimizer(0.01)train_step = my_opt.minimize(loss)# 初始化变量init = tf.global_variables_initializer()sess.run(init)

#迭代训练loss_vec = []train_accuracy = []test_accuracy = []for i in range(1000):    rand_index = np.random.choice(len(x_vals_train), size=batch_size)    rand_x = x_vals_train[rand_index]    rand_y = np.transpose([y_vals_train[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)    train_acc_temp = sess.run(accuracy, feed_dict={        x_data: x_vals_train,        y_target: np.transpose([y_vals_train])})    train_accuracy.append(train_acc_temp)    test_acc_temp = sess.run(accuracy, feed_dict={        x_data: x_vals_test,        y_target: np.transpose([y_vals_test])})    test_accuracy.append(test_acc_temp)

# 抽取系数和截距[[a1], [a2]] = sess.run(A)[[b]] = sess.run(b)slope = -a2/a1y_intercept = b/a1x1_vals = [d[1] for d in x_vals]# best_fit = []for i in x1_vals:    best_fit.append(slope*i+y_intercept)setosa_x = [d[1] for i, d in enumerate(x_vals) if y_vals[i] == 1]setosa_y = [d[0] for i, d in enumerate(x_vals) if y_vals[i] == 1]not_setosa_x = [d[1] for i, d in enumerate(x_vals) if y_vals[i] == -1]not_setosa_y = [d[0] for i, d in enumerate(x_vals) if y_vals[i] == -1]

%matplotlib inline# 展示分类结果plt.plot(setosa_x, setosa_y, 'o', label='得病')plt.plot(not_setosa_x, not_setosa_y, 'x', label='没得病')plt.plot(x1_vals, best_fit, 'r-', label='线性分类器', linewidth=3)plt.ylim([0, 10])plt.legend(loc='lower right')plt.title('细胞大小和细胞颜色深度')plt.xlabel('细胞大小')plt.ylabel('细胞颜色深度')plt.show()# 展示训练和测试精度plt.plot(train_accuracy, 'k-', label='训练精度')plt.plot(test_accuracy, 'r--', label='测试精度')plt.title('训练集和测试集精度')plt.xlabel('迭代次数')plt.ylabel('精度')plt.legend(loc='lower right')plt.show()# 损失函数效果plt.plot(loss_vec, 'k-')plt.title('损失误差/迭代次数')plt.xlabel('迭代次数')plt.ylabel('损失误差')plt.show()

分类结果为：

训练损失误差为：

精度为：

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参考：《Tensorflow Machine Learning cookbook》