graph attention network（ICLR2018）官方代码详解（te4nsorflow）

论文地址：https://arxiv.org/abs/1710.10903

代码地址： https://github.com/Diego999/pyGAT

我并没有完整看过这篇论文，但是在大致了解其原理之后就直接看了代码= =。

接下来我将从代码的整个流程开始讲解，首先解析的是不用稀疏矩阵存储的：

使用的数据集：Cora dataset

Cora数据集简要介绍：

图节点数：2708

每个节点的特征维度：1433

邻接矩阵：(2708,2708)，关系表示的是论文之间的引用关系

类别数：7

目录结构：

相关的包：

import numpy as np
import pickle as pkl
import networkx as nx
import scipy.sparse as sp
from scipy.sparse.linalg.eigen.arpack import eigsh
import sys
import time
import numpy as np
import tensorflow as tf

网络需要的数据是什么？

在utils文件下的process.py中：

def load_data(dataset_str): # {'pubmed', 'citeseer', 'cora'}
    """Load data."""
    names = ['x', 'y', 'tx', 'ty', 'allx', 'ally', 'graph']
    objects = []
    for i in range(len(names)):
        with open("data/ind.{}.{}".format(dataset_str, names[i]), 'rb') as f:
            if sys.version_info > (3, 0):
                objects.append(pkl.load(f, encoding='latin1'))
            else:
                objects.append(pkl.load(f))

    x, y, tx, ty, allx, ally, graph = tuple(objects)
    test_idx_reorder = parse_index_file("data/ind.{}.test.index".format(dataset_str))
    test_idx_range = np.sort(test_idx_reorder)

    if dataset_str == 'citeseer':
        # Fix citeseer dataset (there are some isolated nodes in the graph)
        # Find isolated nodes, add them as zero-vecs into the right position
        test_idx_range_full = range(min(test_idx_reorder), max(test_idx_reorder)+1)
        tx_extended = sp.lil_matrix((len(test_idx_range_full), x.shape[1]))
        tx_extended[test_idx_range-min(test_idx_range), :] = tx
        tx = tx_extended
        ty_extended = np.zeros((len(test_idx_range_full), y.shape[1]))
        ty_extended[test_idx_range-min(test_idx_range), :] = ty
        ty = ty_extended

    features = sp.vstack((allx, tx)).tolil()
    features[test_idx_reorder, :] = features[test_idx_range, :]
    adj = nx.adjacency_matrix(nx.from_dict_of_lists(graph))

    labels = np.vstack((ally, ty))
    labels[test_idx_reorder, :] = labels[test_idx_range, :]

    idx_test = test_idx_range.tolist()
    idx_train = range(len(y))
    idx_val = range(len(y), len(y)+500)

    train_mask = sample_mask(idx_train, labels.shape[0])
    val_mask = sample_mask(idx_val, labels.shape[0])
    test_mask = sample_mask(idx_test, labels.shape[0])

    y_train = np.zeros(labels.shape)
    y_val = np.zeros(labels.shape)
    y_test = np.zeros(labels.shape)
    y_train[train_mask, :] = labels[train_mask, :]
    y_val[val_mask, :] = labels[val_mask, :]
    y_test[test_mask, :] = labels[test_mask, :]

    print(adj.shape)
    print(features.shape)

    return adj, features, y_train, y_val, y_test, train_mask, val_mask, test_mask

不管怎么变化，我们需要得到的是：

邻接矩阵：(2708,2708)，需要注意的是邻接矩阵是由nx.adjacency_matrix(nx.from_dict_of_lists(graph))获得，其中graph是引用关系组成的字典，比如：

{
    1:[2,3],
    4:[6,7,8],
}

还需要注意的是该函数返回的稀疏矩阵的存储，是一个coc_matrix：

  (0, 1)     1
  (0, 30)    1
  (0, 33)    1
  (0, 99)    1

第一个元组表示不为0的值在数组中出现的(行、列)，第二个值表示具体的值。看一个例子：

三要素:数据、行,列索引、形状。

特征：(2708,1433)

训练集、验证集、测试集标签：维度都是(2708,7).。注意：tensorflow中的标签需要进行one-hot编码，才能够使用交叉熵进行计算，而pytorch中是不用的。

掩码：掩码的作用就是选取部分节点进行训练、测试和验证，具体操作是：

    idx_test = test_idx_range.tolist()
    idx_train = range(len(y))
    idx_val = range(len(y), len(y)+500)

    train_mask = sample_mask(idx_train, labels.shape[0])
    val_mask = sample_mask(idx_val, labels.shape[0])
    test_mask = sample_mask(idx_test, labels.shape[0])

其中sample_mask函数代码，位于process.py中：

def sample_mask(idx, l):
    """Create mask."""
    mask = np.zeros(l)
    mask[idx] = 1
    return np.array(mask, dtype=np.bool)

也就是先根据l的大小生成一个形状相同的数组，然后根据Idx的值将指定行的值变为True。请看以下例子：

如何对初始数据进行处理？ 

adj, features, y_train, y_val, y_test, train_mask, val_mask, test_mask = process.load_data(dataset)
features, spars = process.preprocess_features(features)

nb_nodes = features.shape[0] #节点数
ft_size = features.shape[1] #特征维度
nb_classes = y_train.shape[1] #类别数

adj = adj.todense()

features = features[np.newaxis]
adj = adj[np.newaxis]
y_train = y_train[np.newaxis]
y_val = y_val[np.newaxis]
y_test = y_test[np.newaxis]
train_mask = train_mask[np.newaxis]
val_mask = val_mask[np.newaxis]
test_mask = test_mask[np.newaxis]

biases = process.adj_to_bias(adj, [nb_nodes], nhood=1)

使用process.preprocess_features(features)对特征进行处理：

def preprocess_features(features):
    """Row-normalize feature matrix and convert to tuple representation"""
    rowsum = np.array(features.sum(1))
    r_inv = np.power(rowsum, -1).flatten()
    r_inv[np.isinf(r_inv)] = 0.
    r_mat_inv = sp.diags(r_inv)
    features = r_mat_inv.dot(features)
    return features.todense(), sparse_to_tuple(features)

我们获得的features是由：sp.vstack((allx, tx)).tolil()得到的，也就是一个lil_matrix。lil_matrix基于行连接存储的稀疏矩阵，看以下例子：

回到上面对特征进行处理的函数，具体步骤为：

• 对每一行求和
• 计算每个值的倒数，然后展开成一维数组
• 将inf类型的值置为0
• 生成一个对角矩阵，对角的值为一维数组的值，其余的为0
• 最后与特征进行np.matmul
• 使用todense()函数lil_matrix还原为原始矩阵

接下来我们同样将adj转换为原始的矩阵，并且使用np.newaxis新增一个维度：

features；(2708,1433) ->(1,2708,1433)

adj：(2708,2708) -> (1,2708,2708)

y_train：(2708,7) -> (1,2708,7)

y_val：(2708,7) -> (1,2708,7)

y_test：(2708,7) -> (1,2708,7)

train_mask：(2708,.) -> (1,2708)
val_mask：(2708,.) -> (1,2708)

test_mask：(2708,.) -> (1,2708)

最后是：biases = process.adj_to_bias(adj, [nb_nodes], nhood=1)

看一下adj_to_bias(adj, [nb_nodes], nhood=1)函数：感觉是

def adj_to_bias(adj, sizes, nhood=1):
    nb_graphs = adj.shape[0] #1
    mt = np.empty(adj.shape) #(1，2708,2708)
    for g in range(nb_graphs): #range(1)
        mt[g] = np.eye(adj.shape[1]) #mt[0] = np.eye(2708) -> (2708,2708)
        for _ in range(nhood): #range(1)
            mt[g] = np.matmul(mt[g], (adj[g] + np.eye(adj.shape[1]))) #np.matmul((2708,2708),((2708,2708)+(2708,2708)))->(2708,2708)
        for i in range(sizes[g]): #range(2078)
            for j in range(sizes[g]): #range(2078)
                if mt[g][i][j] > 0.0:
                    mt[g][i][j] = 1.0
    return -1e9 * (1.0 - mt)

np.eye()：生成一个对角矩阵，对角的值为1，其余地方为0。

这里要注意np.matmul的用法，看一个例子：

对应步骤：

• 生成一个空(1,2708,2708)的矩阵mt
• 将mt[0]，也就是(2708,2708)变为对角值为1的对角矩阵
• 该对角矩阵和(adj[g] + np.eye(adj.shape[1]))进行np.matmul
• 然后将mt中大于0的元素置为1
• 最后返回-1e9*(1-mt)，形状为(1,2708,2708)

可以看出该函数的作用就是为不相邻的两个节点间添加一个偏置项。

GAT模型是怎么建立的？

多头注意力：

在models文件夹下的gat.py中：

import numpy as np
import tensorflow as tf

from utils import layers
from models.base_gattn import BaseGAttN

class GAT(BaseGAttN):
    def inference(inputs, nb_classes, nb_nodes, training, attn_drop, ffd_drop,
            bias_mat, hid_units, n_heads, activation=tf.nn.elu, residual=False):
        attns = []
        for _ in range(n_heads[0]):
            attns.append(layers.attn_head(inputs, bias_mat=bias_mat,
                out_sz=hid_units[0], activation=activation,
                in_drop=ffd_drop, coef_drop=attn_drop, residual=False))
        h_1 = tf.concat(attns, axis=-1)
        for i in range(1, len(hid_units)):
            h_old = h_1
            attns = []
            for _ in range(n_heads[i]):
                attns.append(layers.attn_head(h_1, bias_mat=bias_mat,
                    out_sz=hid_units[i], activation=activation,
                    in_drop=ffd_drop, coef_drop=attn_drop, residual=residual))
            h_1 = tf.concat(attns, axis=-1)
        out = []
        for i in range(n_heads[-1]):
            out.append(layers.attn_head(h_1, bias_mat=bias_mat,
                out_sz=nb_classes, activation=lambda x: x,
                in_drop=ffd_drop, coef_drop=attn_drop, residual=False))
        logits = tf.add_n(out) / n_heads[-1]

        return logits

相关参数：

hid_units=[8]

n_heads=[8，1]

每个注意力头的输出为：(1,2708,8)，h_1将每个注意头(共8个)的输出进行拼接得到：(1,2708,64)。

根据len(hid_units)=1，因此第2个for循环是没有被执行的，然后再进行一次多头注意力(1个注意力头)得到的输出out就是：(1,2708,7)

每一个注意力头：attn_head

接下来是重头，具体的注意力的实现，论文的核心也就是在这里了。

在utils文件夹下的layers.py中：

def attn_head(seq, out_sz, bias_mat, activation, in_drop=0.0, coef_drop=0.0, residual=False):
    with tf.name_scope('my_attn'):
        if in_drop != 0.0:
            seq = tf.nn.dropout(seq, 1.0 - in_drop)

        seq_fts = tf.layers.conv1d(seq, out_sz, 1, use_bias=False)

        # simplest self-attention possible
        f_1 = tf.layers.conv1d(seq_fts, 1, 1)
        f_2 = tf.layers.conv1d(seq_fts, 1, 1)
        logits = f_1 + tf.transpose(f_2, [0, 2, 1])
        coefs = tf.nn.softmax(tf.nn.leaky_relu(logits) + bias_mat)

        if coef_drop != 0.0:
            coefs = tf.nn.dropout(coefs, 1.0 - coef_drop)
        if in_drop != 0.0:
            seq_fts = tf.nn.dropout(seq_fts, 1.0 - in_drop)

        vals = tf.matmul(coefs, seq_fts)
        ret = tf.contrib.layers.bias_add(vals)

        # residual connection
        if residual:
            if seq.shape[-1] != ret.shape[-1]:
                ret = ret + conv1d(seq, ret.shape[-1], 1) # activation
            else:
                ret = ret + seq

        return activation(ret)  # activation

有关于dropout和残差连接就不细讲了，一个是为了缓解过拟合问题，一个是为了缓解梯度消失问题。

步骤如下：

• 输入features：(1,2708,1433)
• 第一步对特征features卷积，得到seq_fts：(1,2708,8)
• 第二步分别对seq_fts进行卷积，得到f_1：(1,2708,1)，f_2：(1,2708,1)
• 第三步将f_2调整形状为:(1,1,2708)，利用广播机制与f_1相加得到logits：(1,2708,2708)
• 第四步加上偏置项biases_mat，我们注意到偏置项的值很小，是为了过滤掉和该节点不相邻的节点，因为考虑的是某节点和其邻居节点之间的注意力。并使用leakyrelu进行激活，最后经过softmax生成注意力得分coefs：(1,2708,2708)
• 第五步将注意力得分与seq_fts进行np.matmul得到带注意力得分的vals：(1,2708,8)
• 第六步：ret = tf.contrib.layers.bias_add(vals)，这里我运行时是报错的，说没有什么TPU之类的，我将其注释掉了才运行成功（tensorflow1.14）
• 最后将ret进行激活：tf.nn.elu

那么为什么要这么做呢？

主要是如何对注意力进行建模，实际上f_1+f_2也就是(1,2708,1) * (1,1,2708)，这里就计算了每个节点和其它节点之间的得分。

其它的一些相关？

GAT类继承了BasicAttn，我们看下BasicAttn类：

class BaseGAttN:
    def loss(logits, labels, nb_classes, class_weights):
        sample_wts = tf.reduce_sum(tf.multiply(tf.one_hot(labels, nb_classes), class_weights), axis=-1)
        xentropy = tf.multiply(tf.nn.sparse_softmax_cross_entropy_with_logits(
                labels=labels, logits=logits), sample_wts)
        return tf.reduce_mean(xentropy, name='xentropy_mean')

    def training(loss, lr, l2_coef):
        # weight decay
        vars = tf.trainable_variables()
        lossL2 = tf.add_n([tf.nn.l2_loss(v) for v in vars if v.name not
                           in ['bias', 'gamma', 'b', 'g', 'beta']]) * l2_coef

        # optimizer
        opt = tf.train.AdamOptimizer(learning_rate=lr)

        # training op
        train_op = opt.minimize(loss+lossL2)

        return train_op

    def preshape(logits, labels, nb_classes):
        new_sh_lab = [-1]
        new_sh_log = [-1, nb_classes]
        log_resh = tf.reshape(logits, new_sh_log)
        lab_resh = tf.reshape(labels, new_sh_lab)
        return log_resh, lab_resh

    def confmat(logits, labels):
        preds = tf.argmax(logits, axis=1)
        return tf.confusion_matrix(labels, preds)

##########################
# Adapted from tkipf/gcn #
##########################

    def masked_softmax_cross_entropy(logits, labels, mask):
        """Softmax cross-entropy loss with masking."""
        loss = tf.nn.softmax_cross_entropy_with_logits(logits=logits, labels=labels)
        mask = tf.cast(mask, dtype=tf.float32)
        mask /= tf.reduce_mean(mask)
        loss *= mask
        return tf.reduce_mean(loss)

    def masked_sigmoid_cross_entropy(logits, labels, mask):
        """Softmax cross-entropy loss with masking."""
        labels = tf.cast(labels, dtype=tf.float32)
        loss = tf.nn.sigmoid_cross_entropy_with_logits(logits=logits, labels=labels)
        loss=tf.reduce_mean(loss,axis=1)
        mask = tf.cast(mask, dtype=tf.float32)
        mask /= tf.reduce_mean(mask)
        loss *= mask
        return tf.reduce_mean(loss)

    def masked_accuracy(logits, labels, mask):
        """Accuracy with masking."""
        correct_prediction = tf.equal(tf.argmax(logits, 1), tf.argmax(labels, 1))
        accuracy_all = tf.cast(correct_prediction, tf.float32)
        mask = tf.cast(mask, dtype=tf.float32)
        mask /= tf.reduce_mean(mask)
        accuracy_all *= mask
        return tf.reduce_mean(accuracy_all)

    def micro_f1(logits, labels, mask):
        """Accuracy with masking."""
        predicted = tf.round(tf.nn.sigmoid(logits))

        # Use integers to avoid any nasty FP behaviour
        predicted = tf.cast(predicted, dtype=tf.int32)
        labels = tf.cast(labels, dtype=tf.int32)
        mask = tf.cast(mask, dtype=tf.int32)

        # expand the mask so that broadcasting works ([nb_nodes, 1])
        mask = tf.expand_dims(mask, -1)

        # Count true positives, true negatives, false positives and false negatives.
        tp = tf.count_nonzero(predicted * labels * mask)
        tn = tf.count_nonzero((predicted - 1) * (labels - 1) * mask)
        fp = tf.count_nonzero(predicted * (labels - 1) * mask)
        fn = tf.count_nonzero((predicted - 1) * labels * mask)

        # Calculate accuracy, precision, recall and F1 score.
        precision = tp / (tp + fp)
        recall = tp / (tp + fn)
        fmeasure = (2 * precision * recall) / (precision + recall)
        fmeasure = tf.cast(fmeasure, tf.float32)
        return fmeasure

这里面定义了训练循环，损失计算，模型评价指标等等。

最后是计算图以及session：

with tf.Graph().as_default():
    with tf.name_scope('input'):
        ftr_in = tf.placeholder(dtype=tf.float32, shape=(batch_size, nb_nodes, ft_size))
        bias_in = tf.placeholder(dtype=tf.float32, shape=(batch_size, nb_nodes, nb_nodes))
        lbl_in = tf.placeholder(dtype=tf.int32, shape=(batch_size, nb_nodes, nb_classes))
        msk_in = tf.placeholder(dtype=tf.int32, shape=(batch_size, nb_nodes))
        attn_drop = tf.placeholder(dtype=tf.float32, shape=())
        ffd_drop = tf.placeholder(dtype=tf.float32, shape=())
        is_train = tf.placeholder(dtype=tf.bool, shape=())

    logits = model.inference(ftr_in, nb_classes, nb_nodes, is_train,
                                attn_drop, ffd_drop,
                                bias_mat=bias_in,
                                hid_units=hid_units, n_heads=n_heads,
                                residual=residual, activation=nonlinearity)
    log_resh = tf.reshape(logits, [-1, nb_classes])
    lab_resh = tf.reshape(lbl_in, [-1, nb_classes])
    msk_resh = tf.reshape(msk_in, [-1])
    loss = model.masked_softmax_cross_entropy(log_resh, lab_resh, msk_resh)
    accuracy = model.masked_accuracy(log_resh, lab_resh, msk_resh)

    train_op = model.training(loss, lr, l2_coef)

    saver = tf.train.Saver()

    init_op = tf.group(tf.global_variables_initializer(), tf.local_variables_initializer())

    vlss_mn = np.inf
    vacc_mx = 0.0
    curr_step = 0

    with tf.Session() as sess:
        sess.run(init_op)

        train_loss_avg = 0
        train_acc_avg = 0
        val_loss_avg = 0
        val_acc_avg = 0

        for epoch in range(nb_epochs):
            tr_step = 0
            tr_size = features.shape[0]

            while tr_step * batch_size < tr_size:
                _, loss_value_tr, acc_tr = sess.run([train_op, loss, accuracy],
                    feed_dict={
                        ftr_in: features[tr_step*batch_size:(tr_step+1)*batch_size],
                        bias_in: biases[tr_step*batch_size:(tr_step+1)*batch_size],
                        lbl_in: y_train[tr_step*batch_size:(tr_step+1)*batch_size],
                        msk_in: train_mask[tr_step*batch_size:(tr_step+1)*batch_size],
                        is_train: True,
                        attn_drop: 0.6, ffd_drop: 0.6})
                train_loss_avg += loss_value_tr
                train_acc_avg += acc_tr
                tr_step += 1

            vl_step = 0
            vl_size = features.shape[0]

            while vl_step * batch_size < vl_size:
                loss_value_vl, acc_vl = sess.run([loss, accuracy],
                    feed_dict={
                        ftr_in: features[vl_step*batch_size:(vl_step+1)*batch_size],
                        bias_in: biases[vl_step*batch_size:(vl_step+1)*batch_size],
                        lbl_in: y_val[vl_step*batch_size:(vl_step+1)*batch_size],
                        msk_in: val_mask[vl_step*batch_size:(vl_step+1)*batch_size],
                        is_train: False,
                        attn_drop: 0.0, ffd_drop: 0.0})
                val_loss_avg += loss_value_vl
                val_acc_avg += acc_vl
                vl_step += 1

            print('Training: loss = %.5f, acc = %.5f | Val: loss = %.5f, acc = %.5f' %
                    (train_loss_avg/tr_step, train_acc_avg/tr_step,
                    val_loss_avg/vl_step, val_acc_avg/vl_step))

            if val_acc_avg/vl_step >= vacc_mx or val_loss_avg/vl_step <= vlss_mn:
                if val_acc_avg/vl_step >= vacc_mx and val_loss_avg/vl_step <= vlss_mn:
                    vacc_early_model = val_acc_avg/vl_step
                    vlss_early_model = val_loss_avg/vl_step
                    saver.save(sess, checkpt_file)
                vacc_mx = np.max((val_acc_avg/vl_step, vacc_mx))
                vlss_mn = np.min((val_loss_avg/vl_step, vlss_mn))
                curr_step = 0
            else:
                curr_step += 1
                if curr_step == patience:
                    print('Early stop! Min loss: ', vlss_mn, ', Max accuracy: ', vacc_mx)
                    print('Early stop model validation loss: ', vlss_early_model, ', accuracy: ', vacc_early_model)
                    break

            train_loss_avg = 0
            train_acc_avg = 0
            val_loss_avg = 0
            val_acc_avg = 0

        saver.restore(sess, checkpt_file)

        ts_size = features.shape[0]
        ts_step = 0
        ts_loss = 0.0
        ts_acc = 0.0

        while ts_step * batch_size < ts_size:
            loss_value_ts, acc_ts = sess.run([loss, accuracy],
                feed_dict={
                    ftr_in: features[ts_step*batch_size:(ts_step+1)*batch_size],
                    bias_in: biases[ts_step*batch_size:(ts_step+1)*batch_size],
                    lbl_in: y_test[ts_step*batch_size:(ts_step+1)*batch_size],
                    msk_in: test_mask[ts_step*batch_size:(ts_step+1)*batch_size],
                    is_train: False,
                    attn_drop: 0.0, ffd_drop: 0.0})
            ts_loss += loss_value_ts
            ts_acc += acc_ts
            ts_step += 1

        print('Test loss:', ts_loss/ts_step, '; Test accuracy:', ts_acc/ts_step)

        sess.close()

这里需要注意的是，虽然目前tensorflow出了2.x版本之后就简化了很多，但是之前1.x版本还是需要了解的。以上代码就是1.x版本，1.x版本的tensorflow的一般分为以下步骤：

（1）利用类似python的上下文管理器定义计算图；

（2）为计算图中的一些变量定义占位符；

（3）定义损失、模型、评价指标、训练循环、初始化参数、保存模型等；

（4）将训练流程放入到session中，然后在相关的位置喂入实际的数据；

总结：

最后还是做个总结吧。能看到这里相信你对GAT的整个脉络已经了解的很清楚了，顺带还了解了其它的一些库的用法。如何才能真正的去弄懂一篇论文，每个人都有其自己的方式，包括去看原论文，去网上找相应的博客，其实在有大致了解之后去看源代码不失为一种好的办法。对于代码量比较少而言，可以像我这样一步一步的去剖析每行代码的作用，但是对于庞大的代码而言，还是要根据功能点划分代码块，针对于不同功能的代码块花不同的精力去研究。

由于我的水平有限，其中难免有理解不正确的地方，欢迎指出。