由多个带有S型激活函数的隐含层及一个线性输出层构成的自编码器，称为线性编码器。
实例：提取图片的二维特征，并利用二维特征还原图片。将MNIST图片压缩成二维数据，这样也可以在直角坐标系上将其显示出来，让读者更形象地了解自编码网络在特征提取方面的功能。
import tensorflow as tf import numpy as np import matplotlib.pyplot as plt # 导入 MINST 数据集 from tensorflow.examples.tutorials.mnist import input_data mnist = input_data.read_data_sets("/data/", one_hot=True) # 参数设置 learning_rate = 0.01 n_hidden_1 = 256 n_hidden_2 = 64 n_hidden_3 = 16 n_hidden_4 = 2 n_input = 784 # 28 x 28 x = tf.placeholder("float", [None, n_input]) y = x # 参数 weights = { "encoder_h1": tf.Variable(tf.random_normal([n_input, n_hidden_1])), "encoder_h2": tf.Variable(tf.random_normal([n_hidden_1, n_hidden_2])), "encoder_h3": tf.Variable(tf.random_normal([n_hidden_2, n_hidden_3])), "encoder_h4": tf.Variable(tf.random_normal([n_hidden_3, n_hidden_4])), "decoder_h1": tf.Variable(tf.random_normal([n_hidden_4, n_hidden_3])), "decoder_h2": tf.Variable(tf.random_normal([n_hidden_3, n_hidden_2])), "decoder_h3": tf.Variable(tf.random_normal([n_hidden_2, n_hidden_1])), "decoder_h4": tf.Variable(tf.random_normal([n_hidden_1, n_input])), } biases = { 'encoder_b1': tf.Variable(tf.zeros([n_hidden_1])), 'encoder_b2': tf.Variable(tf.zeros([n_hidden_2])), 'encoder_b3': tf.Variable(tf.zeros([n_hidden_3])), 'encoder_b4': tf.Variable(tf.zeros([n_hidden_4])), 'decoder_b1': tf.Variable(tf.zeros([n_hidden_3])), 'decoder_b2': tf.Variable(tf.zeros([n_hidden_2])), 'decoder_b3': tf.Variable(tf.zeros([n_hidden_1])), 'decoder_b4': tf.Variable(tf.zeros([n_input])), } # 编码 def encoder(x): layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights["encoder_h1"]), biases["encoder_b1"])) layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights["encoder_h2"]), biases["encoder_b2"])) layer_3 = tf.nn.sigmoid(tf.add(tf.matmul(layer_2, weights["encoder_h3"]), biases["encoder_b3"])) layer_4 = tf.add(tf.matmul(layer_3, weights["encoder_h4"]), biases["encoder_b4"]) # 线性层 return layer_4 # 解码 def decoder(x): layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights["decoder_h1"]), biases["decoder_b1"])) layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights["decoder_h2"]), biases["decoder_b2"])) layer_3 = tf.nn.sigmoid(tf.add(tf.matmul(layer_2, weights["decoder_h3"]), biases["decoder_b3"])) layer_4 = tf.nn.sigmoid(tf.add(tf.matmul(layer_3, weights["decoder_h4"]), biases["decoder_b4"])) return layer_4 # 构建模型 encoder_op = encoder(x) y_pred = decoder(encoder_op) # 损失函数 cost = tf.reduce_mean(tf.pow(y - y_pred, 2)) optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost) #训练 training_epochs = 20 batch_size = 256 display_step = 1 with tf.Session() as sess: sess.run(tf.global_variables_initializer()) total_batch = int(mnist.train.num_examples/batch_size) # 开始训练 for epoch in range(training_epochs): # 迭代 for i in range(total_batch): batch_xs, batch_ys = mnist.train.next_batch(batch_size) _, c = sess.run([optimizer, cost], feed_dict={x: batch_xs}) # 训练模型 if epoch % display_step == 0: print("Epoch:", "d"%(epoch+1), "cost=", "{:.9f}".format(c)) print("Done") # 可视化结果 show_num = 10 # 10张图片 encode_decode = sess.run(y_pred, feed_dict={x: mnist.test.images[:show_num]}) f, a = plt.subplots(2, 10, figsize=(10, 2)) for i in range(show_num): a[0][i].imshow(np.reshape(mnist.test.images[i], (28,28))) a[1][i].imshow(np.reshape(encode_decode[i], (28,28))) plt.show() # 显示二维图像信息 aa = [np.argmax(l) for l in mnist.test.labels] # 将onehot转成数值 encoder_result = sess.run(encoder_op, feed_dict={x: mnist.test.images}) plt.scatter(encoder_result[:, 0], encoder_result[:, 1], c=aa) plt.colorbar() plt.show()可以看出输出与真实图像大体一样，但有几个还有偏差
以上是0-9图像在二维坐标系中显示分别，可以看出分布比较聚集。
所以一般来说用自编码网络将数据降维之后的数据更有利于进行分类处理
