图神经网络的研究与图嵌入或网络嵌入密切相关，图嵌入或网络嵌入是数据挖掘和机器学习界日益关注的另一个课题。图嵌入旨在通过保留图的网络拓扑结构和节点内容信息，将图中顶点表示为低维向量，以便使用简单的机器学习算法（例如，支持向量机分类）进行处理。许多图嵌入算法通常是无监督的算法，它们可以大致可以划分为三个类别，即矩阵分解、随机游走和深度学习方法。同时图嵌入的深度学习方法也属于图神经网络，包括基于图自动编码器的算法（如DNGR和SDNE）和无监督训练的图卷积神经网络（如GraphSage）。——https://zhuanlan.zhihu.com/p/75307407
下面给出一个图神经网络TensorFlow的实现，代码来自https://github.com/Ivan0131/gnn_demo。
import tensorflow as tfimport numpy as npimport gnn.gnn_utils as gnn_utilsdata_path = "./data"set_name = "sub_15_7_200"# 训练集inp, arcnode, nodegraph, nodein, labels, _ = gnn_utils.set_load_general(data_path, "train", set_name=set_name)inp = [a[:, 1:] for a in inp]# 验证集inp_val, arcnode_val, nodegraph_val, nodein_val, labels_val, _ = gnn_utils.set_load_general(data_path, "validation", set_name=set_name)inp_val = [a[:, 1:] for a in inp_val]input_dim = len(inp[0][0])state_dim = 10output_dim = 2state_threshold = 0.001max_iter = 50tf.compat.v1.disable_eager_execution()tf.reset_default_graph()comp_inp = tf.placeholder(tf.float32, shape=(None, input_dim), name="input")y = tf.placeholder(tf.float32, shape=(None, output_dim), name="target")state = tf.placeholder(tf.float32, shape=(None, state_dim), name="state")state_old = tf.placeholder(tf.float32, shape=(None, state_dim), name="old_state")ArcNode = tf.sparse_placeholder(tf.float32, name="ArcNode")def f_w(inp): with tf.variable_scope('State_net'): layer1 = tf.layers.dense(inp, 5, activation=tf.nn.sigmoid) layer2 = tf.layers.dense(layer1, state_dim, activation=tf.nn.sigmoid) return layer2def g_w(inp): with tf.variable_scope('Output_net'): layer1 = tf.layers.dense(inp, 5, activation=tf.nn.sigmoid) layer2 = tf.layers.dense(layer1, output_dim, activation=None) return layer2def convergence(a, state, old_state, k): with tf.variable_scope('Convergence'): # assign current state to old state old_state = state # 获取子结点上一个时刻的状态 # grub states of neighboring node gat = tf.gather(old_state, tf.cast(a[:, 0], tf.int32)) print(a[:, 0]) # 去除第一列，即子结点的id # slice to consider only label of the node and that of it's neighbor # sl = tf.slice(a, [0, 1], [tf.shape(a)[0], tf.shape(a)[1] - 1]) # equivalent code sl = a[:, 1:] # 将子结点上一个时刻的状态放到最后一列 # concat with retrieved state inp = tf.concat([sl, gat], axis=1) print('inp', inp) # evaluate next state and multiply by the arch-node conversion matrix to obtain per-node states # 计算子结点对父结点状态的贡献 layer1 = f_w(inp) # 聚合子结点对父结点状态的贡献，得到当前时刻的父结点的状态 print('ArcNode', ArcNode) state = tf.sparse_tensor_dense_matmul(ArcNode, layer1) # update the iteration counter k = k + 1 return a, state, old_state, kdef condition(a, state, old_state, k): # evaluate condition on the convergence of the state with tf.variable_scope('condition'): # 检查当前状态和上一个时刻的状态的欧式距离是否小于阈值 # evaluate distance by state(t) and state(t-1) outDistance = tf.sqrt(tf.reduce_sum(tf.square(tf.subtract(state, old_state)), 1) + 1e-10) # vector showing item converged or not (given a certain threshold) checkDistanceVec = tf.greater(outDistance, state_threshold) print(outDistance) print(checkDistanceVec) c1 = tf.reduce_any(checkDistanceVec) print(c1) # 是否达到最大迭代次数 c2 = tf.less(k, max_iter) print(c2) return tf.logical_and(c1, c2)# 迭代计算，直到状态达到稳定状态with tf.variable_scope('Loop'): k = tf.constant(0) res, st, old_st, num = tf.while_loop(condition, convergence, [comp_inp, state, state_old, k]) out = g_w(st)loss = tf.reduce_mean(tf.nn.softmax_cross_entropy_with_logits_v2(labels=y, logits=out))accuracy = tf.reduce_mean(tf.cast(tf.equal(tf.argmax(out, 1), tf.argmax(y, 1)), dtype=tf.float32))optimizer = tf.train.AdamOptimizer(0.001)grads = optimizer.compute_gradients(loss)train_op = optimizer.apply_gradients(grads, name='train_op')# 模型训练num_epoch = 5000# 训练集placeholder输入arcnode_train = tf.SparseTensorValue(indices=arcnode[0].indices, values=arcnode[0].values, dense_shape=arcnode[0].dense_shape)fd_train = {comp_inp: inp[0], state: np.zeros((arcnode[0].dense_shape[0], state_dim)), state_old: np.ones((arcnode[0].dense_shape[0], state_dim)), ArcNode: arcnode_train, y: labels}# 验证集placeholder输入arcnode_valid = tf.SparseTensorValue(indices=arcnode_val[0].indices, values=arcnode_val[0].values, dense_shape=arcnode_val[0].dense_shape)fd_valid = {comp_inp: inp_val[0], state: np.zeros((arcnode_val[0].dense_shape[0], state_dim)), state_old: np.ones((arcnode_val[0].dense_shape[0], state_dim)), ArcNode: arcnode_valid, y: labels_val}with tf.Session() as sess: sess.run(tf.global_variables_initializer()) sess.run(tf.local_variables_initializer()) for i in range(0, num_epoch): _, loss_val, accuracy_val = sess.run( [train_op, loss, accuracy], feed_dict=fd_train) if i % 100 == 0: loss_valid_val, accuracy_valid_val = sess.run( [loss, accuracy], feed_dict=fd_valid) print( "iter %st training loss: %s,t training accuracy: %s,t validation loss: %s,t validation accuracy: %s" % (i, loss_val, accuracy_val, loss_valid_val, accuracy_valid_val))数据集和参考代码：https://github.com/Ivan0131/gnn_demo