Autoencoder降维可视化
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参考技术A 关于高维度数据降维，以前都是使用PCA线性降维或者直接使用pandas的corr函数来找到相关性，但是这种方式的降维都是线性的。Autoencoder可以完成线性的、非线性的降维，提取有效的数据表征。下面是笔者收集展示的三个案例。案例1：3D dataset数据集
1、创建3D数据集
2、创建模型并训练，2个神经元的编码器隐藏层，3个神经元的解码器隐藏层
3、encoder编码器预测实例完成降维
案例2：mnist手写数字
1、定义函数load_mnist导入本地mnist数据集
2、Autoencoder降低到二维
3、AutoEncoder编码器预测新实例得到二维数据，并绘制图形
以上绘制的图形有重叠部分，不便于区分。笔者再次修改模型使用Autoencoder来降低为对应的10维。
使用TNSE再次完成数据降低到二维，这也就可以展开数据集便于可视化。
案例3：fashion_mnist图像
此案例基于 Autoencoder神经网络完成异常检测(样本重构) ，前期的操作就不再展示了。下面是在编码器预测数据之后再次使用t-SNE，能够将高维空间中的数据映射到低维空间中，并保留数据集的局部特性。
2.3AutoEncoder
AutoEncoder是包含一个压缩和解压缩的过程，属于一种无监督学习的降维技术。
神经网络接受大量信息，有时候接受的数据达到上千万，可以通过压缩
提取原图片最具有代表性的信息，压缩输入的信息量，在将缩减后的数据放入神经网络中学习，如此学习起来变得轻松了
自编码在这个时候使用，可以将自编码归为无监督学习，类似于PCA，自编码可以为属性降维
手写体识别代码AutoEncoder
from __future__ import division, print_function, absolute_import import tensorflow as tf import numpy as np import matplotlib.pyplot as plt # Import MNIST data from tensorflow.examples.tutorials.mnist import input_data mnist = input_data.read_data_sets(\'MNIST_data\', one_hot=False) # Visualize decoder setting # Parameters learning_rate = 0.01 training_epochs = 5 batch_size = 256 display_step = 1 examples_to_show = 10 # Network Parameters n_input = 784 # MNIST data input (img shape: 28*28) # tf Graph input (only pictures) X = tf.placeholder("float", [None, n_input]) # hidden layer settings n_hidden_1 = 256 # 1st layer num features n_hidden_2 = 128 # 2nd layer num features 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])), \'decoder_h1\': tf.Variable(tf.random_normal([n_hidden_2, n_hidden_1])), \'decoder_h2\': tf.Variable(tf.random_normal([n_hidden_1, n_input])), } biases = { \'encoder_b1\': tf.Variable(tf.random_normal([n_hidden_1])), \'encoder_b2\': tf.Variable(tf.random_normal([n_hidden_2])), \'decoder_b1\': tf.Variable(tf.random_normal([n_hidden_1])), \'decoder_b2\': tf.Variable(tf.random_normal([n_input])), } # Building the encoder def encoder(x): # Encoder Hidden layer with sigmoid activation #1 layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights[\'encoder_h1\']), biases[\'encoder_b1\'])) # Decoder Hidden layer with sigmoid activation #2 layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights[\'encoder_h2\']), biases[\'encoder_b2\'])) return layer_2 # Building the decoder def decoder(x): # Encoder Hidden layer with sigmoid activation #1 layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights[\'decoder_h1\']), biases[\'decoder_b1\'])) # Decoder Hidden layer with sigmoid activation #2 layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights[\'decoder_h2\']), biases[\'decoder_b2\'])) return layer_2 """ # Visualize encoder setting # Parameters learning_rate = 0.01 # 0.01 this learning rate will be better! Tested training_epochs = 10 batch_size = 256 display_step = 1 # Network Parameters n_input = 784 # MNIST data input (img shape: 28*28) # tf Graph input (only pictures) X = tf.placeholder("float", [None, n_input]) # hidden layer settings n_hidden_1 = 128 n_hidden_2 = 64 n_hidden_3 = 10 n_hidden_4 = 2 #2D show weights = { \'encoder_h1\': tf.Variable(tf.truncated_normal([n_input, n_hidden_1],)), \'encoder_h2\': tf.Variable(tf.truncated_normal([n_hidden_1, n_hidden_2],)), \'encoder_h3\': tf.Variable(tf.truncated_normal([n_hidden_2, n_hidden_3],)), \'encoder_h4\': tf.Variable(tf.truncated_normal([n_hidden_3, n_hidden_4],)), \'decoder_h1\': tf.Variable(tf.truncated_normal([n_hidden_4, n_hidden_3],)), \'decoder_h2\': tf.Variable(tf.truncated_normal([n_hidden_3, n_hidden_2],)), \'decoder_h3\': tf.Variable(tf.truncated_normal([n_hidden_2, n_hidden_1],)), \'decoder_h4\': tf.Variable(tf.truncated_normal([n_hidden_1, n_input],)), } biases = { \'encoder_b1\': tf.Variable(tf.random_normal([n_hidden_1])), \'encoder_b2\': tf.Variable(tf.random_normal([n_hidden_2])), \'encoder_b3\': tf.Variable(tf.random_normal([n_hidden_3])), \'encoder_b4\': tf.Variable(tf.random_normal([n_hidden_4])), \'decoder_b1\': tf.Variable(tf.random_normal([n_hidden_3])), \'decoder_b2\': tf.Variable(tf.random_normal([n_hidden_2])), \'decoder_b3\': tf.Variable(tf.random_normal([n_hidden_1])), \'decoder_b4\': tf.Variable(tf.random_normal([n_input])), } 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\']) return layer_4 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 """ # Construct model encoder_op = encoder(X) decoder_op = decoder(encoder_op) # Prediction y_pred = decoder_op # Targets (Labels) are the input data. y_true = X # Define loss and optimizer, minimize the squared error cost = tf.reduce_mean(tf.pow(y_true - y_pred, 2)) optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost) # Launch the graph with tf.Session() as sess: # tf.initialize_all_variables() no long valid from # 2017-03-02 if using tensorflow >= 0.12 if int((tf.__version__).split(\'.\')[1]) < 12 and int((tf.__version__).split(\'.\')[0]) < 1: init = tf.initialize_all_variables() else: init = tf.global_variables_initializer() sess.run(init) total_batch = int(mnist.train.num_examples/batch_size) # Training cycle for epoch in range(training_epochs): # Loop over all batches for i in range(total_batch): batch_xs, batch_ys = mnist.train.next_batch(batch_size) # max(x) = 1, min(x) = 0 # Run optimization op (backprop) and cost op (to get loss value) _, c = sess.run([optimizer, cost], feed_dict={X: batch_xs}) # Display logs per epoch step if epoch % display_step == 0: print("Epoch:", \'%04d\' % (epoch+1), "cost=", "{:.9f}".format(c)) print("Optimization Finished!") # # Applying encode and decode over test set encode_decode = sess.run( y_pred, feed_dict={X: mnist.test.images[:examples_to_show]}) # Compare original images with their reconstructions f, a = plt.subplots(2, 10, figsize=(10, 2)) for i in range(examples_to_show): 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() # encoder_result = sess.run(encoder_op, feed_dict={X: mnist.test.images}) # plt.scatter(encoder_result[:, 0], encoder_result[:, 1], c=mnist.test.labels) # plt.colorbar() # plt.show()
利用AutoEncoder进行类似于PCA的降维
代码：
from __future__ import division, print_function, absolute_import import tensorflow as tf import numpy as np import matplotlib.pyplot as plt # Import MNIST data from tensorflow.examples.tutorials.mnist import input_data mnist = input_data.read_data_sets(\'MNIST_data\', one_hot=False) """ # Visualize decoder setting # Parameters learning_rate = 0.01 training_epochs = 5 batch_size = 256 display_step = 1 examples_to_show = 10 # Network Parameters n_input = 784 # MNIST data input (img shape: 28*28) # tf Graph input (only pictures) X = tf.placeholder("float", [None, n_input]) # hidden layer settings n_hidden_1 = 256 # 1st layer num features n_hidden_2 = 128 # 2nd layer num features 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])), \'decoder_h1\': tf.Variable(tf.random_normal([n_hidden_2, n_hidden_1])), \'decoder_h2\': tf.Variable(tf.random_normal([n_hidden_1, n_input])), } biases = { \'encoder_b1\': tf.Variable(tf.random_normal([n_hidden_1])), \'encoder_b2\': tf.Variable(tf.random_normal([n_hidden_2])), \'decoder_b1\': tf.Variable(tf.random_normal([n_hidden_1])), \'decoder_b2\': tf.Variable(tf.random_normal([n_input])), } # Building the encoder def encoder(x): # Encoder Hidden layer with sigmoid activation #1 layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights[\'encoder_h1\']), biases[\'encoder_b1\'])) # Decoder Hidden layer with sigmoid activation #2 layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights[\'encoder_h2\']), biases[\'encoder_b2\'])) return layer_2 # Building the decoder def decoder(x): # Encoder Hidden layer with sigmoid activation #1 layer_1 = tf.nn.sigmoid(tf.add(tf.matmul(x, weights[\'decoder_h1\']), biases[\'decoder_b1\'])) # Decoder Hidden layer with sigmoid activation #2 layer_2 = tf.nn.sigmoid(tf.add(tf.matmul(layer_1, weights[\'decoder_h2\']), biases[\'decoder_b2\'])) return layer_2 """ # Visualize encoder setting # Parameters learning_rate = 0.01 # 0.01 this learning rate will be better! Tested training_epochs = 10 batch_size = 256 display_step = 1 # Network Parameters n_input = 784 # MNIST data input (img shape: 28*28) # tf Graph input (only pictures) X = tf.placeholder("float", [None, n_input]) # hidden layer settings n_hidden_1 = 128 n_hidden_2 = 64 n_hidden_3 = 10 n_hidden_4 = 2 #2D show weights = { \'encoder_h1\': tf.Variable(tf.truncated_normal([n_input, n_hidden_1],)), \'encoder_h2\': tf.Variable(tf.truncated_normal([n_hidden_1, n_hidden_2],)), \'encoder_h3\': tf.Variable(tf.truncated_normal([n_hidden_2, n_hidden_3],)), \'encoder_h4\': tf.Variable(tf.truncated_normal([n_hidden_3, n_hidden_4],)), \'decoder_h1\': tf.Variable(tf.truncated_normal([n_hidden_4, n_hidden_3],)), \'decoder_h2\': tf.Variable(tf.truncated_normal([n_hidden_3, n_hidden_2],)), \'decoder_h3\': tf.Variable(tf.truncated_normal([n_hidden_2, n_hidden_1],)), \'decoder_h4\': tf.Variable(tf.truncated_normal([n_hidden_1, n_input],)), } biases = { \'encoder_b1\': tf.Variable(tf.random_normal([n_hidden_1])), \'encoder_b2\': tf.Variable(tf.random_normal([n_hidden_2])), \'encoder_b3\': tf.Variable(tf.random_normal([n_hidden_3])), \'encoder_b4\': tf.Variable(tf.random_normal([n_hidden_4])), \'decoder_b1\': tf.Variable(tf.random_normal([n_hidden_3])), \'decoder_b2\': tf.Variable(tf.random_normal([n_hidden_2])), \'decoder_b3\': tf.Variable(tf.random_normal([n_hidden_1])), \'decoder_b4\': tf.Variable(tf.random_normal([n_input])), } 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\']) return layer_4 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 # Construct model encoder_op = encoder(X) decoder_op = decoder(encoder_op) # Prediction y_pred = decoder_op # Targets (Labels) are the input data. y_true = X # Define loss and optimizer, minimize the squared error cost = tf.reduce_mean(tf.pow(y_true - y_pred, 2)) optimizer = tf.train.AdamOptimizer(learning_rate).minimize(cost) # Launch the graph with tf.Session() as sess: # tf.initialize_all_variables() no long valid from # 2017-03-02 if using tensorflow >= 0.12 if int((tf.__version__).split(\'.\')[1]) < 12 and int((tf.__version__).split(\'.\')[0]) < 1: init = tf.initialize_all_variables() else: init = tf.global_variables_initializer() sess.run(init) total_batch = int(mnist.train.num_examples/batch_size) # Training cycle for epoch in range(training_epochs): # Loop over all batches for i in range(total_batch): batch_xs, batch_ys = mnist.train.next_batch(batch_size) # max(x) = 1, min(x) = 0 # Run optimization op (backprop) and cost op (to get loss value) _, c = sess.run([optimizer, cost], feed_dict={X: batch_xs}) # Display logs per epoch step if epoch % display_step == 0: print("Epoch:", \'%04d\' % (epoch+1), "cost=", "{:.9f}".format(c)) print("Optimization Finished!") # # # Applying encode and decode over test set # encode_decode = sess.run( # y_pred, feed_dict={X: mnist.test.images[:examples_to_show]}) # # Compare original images with their reconstructions # f, a = plt.subplots(2, 10, figsize=(10, 2)) # for i in range(examples_to_show): # 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() encoder_result = sess.run(encoder_op, feed_dict={X: mnist.test.images}) plt.scatter(encoder_result[:, 0], encoder_result[:, 1], c=mnist.test.labels) plt.colorbar() plt.show()
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