图自编码器（GAE）与变分图自编码器（VGAE）python代码

图自编码器（Graph Autoencoder，简称GAE）是一种用于学习图形数据表示的无监督学习方法，它将图形数据表示为低维嵌入向量。变分图自编码器（Variational Graph Autoencoder，简称VGAE）是一种改进的GAE，它使用变分推断来学习潜在嵌入的概率分布。下面是使用Python实现GAE和VGAE的示例代码：

1. GAE代码：

import numpy as np
import tensorflow as tf

class GraphAutoencoder(object):
    def __init__(self, n_input, n_hidden):
        self.n_input = n_input
        self.n_hidden = n_hidden
        self.weights = {
            'encoder': tf.Variable(tf.random_normal([n_input, n_hidden])),
            'decoder': tf.Variable(tf.random_normal([n_hidden, n_input]))
        }
        self.biases = {
            'encoder': tf.Variable(tf.random_normal([n_hidden])),
            'decoder': tf.Variable(tf.random_normal([n_input]))
        }
        self.inputs = tf.placeholder(tf.float32, [None, n_input])
        self.encoder = tf.nn.sigmoid(tf.add(tf.matmul(self.inputs, self.weights['encoder']), self.biases['encoder']))
        self.decoder = tf.nn.sigmoid(tf.add(tf.matmul(self.encoder, self.weights['decoder']), self.biases['decoder']))
        self.cost = tf.reduce_mean(tf.pow(self.inputs - self.decoder, 2))
        self.optimizer = tf.train.AdamOptimizer(learning_rate=0.01).minimize(self.cost)

    def train(self, X, epochs=1000):
        with tf.Session() as sess:
            sess.run(tf.global_variables_initializer())
            for epoch in range(epochs):
                _, cost = sess.run([self.optimizer, self.cost], feed_dict={self.inputs: X})
                if epoch % 100 == 0:
                    print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(cost))
            self.weights['encoder'] = sess.run(self.weights['encoder'])
            self.weights['decoder'] = sess.run(self.weights['decoder'])
            self.biases['encoder'] = sess.run(self.biases['encoder'])
            self.biases['decoder'] = sess.run(self.biases['decoder'])
        return self

    def transform(self, X):
        with tf.Session() as sess:
            sess.run(tf.global_variables_initializer())
            encoder_output = sess.run(self.encoder, feed_dict={self.inputs: X})
        return encoder_output

2. VGAE代码：

import numpy as np
import tensorflow as tf

class VariationalGraphAutoencoder(object):
    def __init__(self, n_input, n_hidden):
        self.n_input = n_input
        self.n_hidden = n_hidden
        self.weights = {
            'encoder_mean': tf.Variable(tf.random_normal([n_input, n_hidden])),
            'encoder_stddev': tf.Variable(tf.random_normal([n_input, n_hidden])),
            'decoder': tf.Variable(tf.random_normal([n_hidden, n_input]))
        }
        self.biases = {
            'encoder_mean': tf.Variable(tf.random_normal([n_hidden])),
            'encoder_stddev': tf.Variable(tf.random_normal([n_hidden])),
            'decoder': tf.Variable(tf.random_normal([n_input]))
        }
        self.inputs = tf.placeholder(tf.float32, [None, n_input])
        self.encoder_mean = tf.add(tf.matmul(self.inputs, self.weights['encoder_mean']), self.biases['encoder_mean'])
        self.encoder_stddev = tf.add(tf.matmul(self.inputs, self.weights['encoder_stddev']), self.biases['encoder_stddev'])
        eps = tf.random_normal(tf.shape(self.encoder_stddev), dtype=tf.float32, mean=0., stddev=1.0,
                               name='epsilon')
        self.encoder_output = tf.add(self.encoder_mean, tf.multiply(tf.sqrt(tf.exp(self.encoder_stddev)), eps))
        self.decoder = tf.nn.sigmoid(
            tf.add(tf.matmul(self.encoder_output, self.weights['decoder']), self.biases['decoder']))
        self.cost = self.get_cost()
        self.optimizer = tf.train.AdamOptimizer(learning_rate=0.01).minimize(self.cost)

    def get_cost(self):
        kl_divergence = -0.5 * tf.reduce_sum(
            1 + 2 * self.encoder_stddev - tf.square(self.encoder_mean) - tf.exp(2 * self.encoder_stddev), 1)
        reconstruction_loss = -tf.reduce_sum(
            self.inputs * tf.log(1e-10 + self.decoder) + (1 - self.inputs) * tf.log(1e-10 + 1 - self.decoder), 1)
        cost = tf.reduce_mean(reconstruction_loss + kl_divergence)
        return cost

    def train(self, X, epochs=1000):
        with tf.Session() as sess:
            sess.run(tf.global_variables_initializer())
            for epoch in range(epochs):
                _, cost = sess.run([self.optimizer, self.cost], feed_dict={self.inputs: X})
                if epoch % 100 == 0:
                    print("Epoch:", '%04d' % (epoch+1), "cost=", "{:.9f}".format(cost))
            self.weights['encoder_mean'] = sess.run(self.weights['encoder_mean'])
            self.weights['encoder_stddev'] = sess.run(self.weights['encoder_stddev'])
            self.weights['decoder'] = sess.run(self.weights['decoder'])
            self.biases['encoder_mean'] = sess.run(self.biases['encoder_mean'])
            self.biases['encoder_stddev'] = sess.run(self.biases['encoder_stddev'])
            self.biases['decoder'] = sess.run(self.biases['decoder'])
        return self

    def transform(self, X):
        with tf.Session() as sess:
            sess.run(tf.global_variables_initializer())
            encoder_output = sess.run(self.encoder_output, feed_dict={self.inputs: X})
        return encoder_output

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