graph attention network（ICLR2018）官方代码详解（tensorflow）-稀疏矩阵版

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我们知道图的邻接矩阵可能是稀疏的，将整个图加载到内存中是十分耗费资源的，因此对邻接矩阵进行存储和计算是很有必要的。

我们已经讲解了图注意力网络的非稀疏矩阵版本，再来弄清其稀疏矩阵版本就轻松了，接下来我们将来看不同之处。

主运行代码在：execute_cora_sparse.py中

同样的，先加载数据：

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

其中adj是coo_matrix类型，features是lil_matrix类型。

对于features，我们最终还是：

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)

将其：

features, spars = process.preprocess_features(features)

转换为原始矩阵。

对于biases：

if sparse:
    biases = process.preprocess_adj_bias(adj)
else:
    adj = adj.todense()
    adj = adj[np.newaxis]
    biases = process.adj_to_bias(adj, [nb_nodes], nhood=1)

如果是稀疏格式的，就调用biases = process.preprocess_adj_bias(adj)：

def preprocess_adj_bias(adj):
    num_nodes = adj.shape[0] #2708
    adj = adj + sp.eye(num_nodes)  # self-loop 给对角上+1
    adj[adj > 0.0] = 1.0 #大于0的值置为1
    if not sp.isspmatrix_coo(adj):
        adj = adj.tocoo()
    adj = adj.astype(np.float32) #类型转换
    indices = np.vstack((adj.col, adj.row)).transpose()  # This is where I made a mistake, I used (adj.row, adj.col) instead
    # return tf.SparseTensor(indices=indices, values=adj.data, dense_shape=adj.shape)
    return indices, adj.data, adj.shape

这里看两个例子：

我们可以通过indices，data，shape来构造一个coo_matrix。

在定义计算图中的占位符时：

if sparse:
            #bias_idx = tf.placeholder(tf.int64)
            #bias_val = tf.placeholder(tf.float32)
            #bias_shape = tf.placeholder(tf.int64)
            bias_in = tf.sparse_placeholder(dtype=tf.float32)
        else:
            bias_in = tf.placeholder(dtype=tf.float32, shape=(batch_size, nb_nodes, nb_nodes))

使用bias_in = tf.sparse_placeholder(dtype=tf.float32)。

再接着就是模型中了，在utils文件夹下的layers.py中：

# Experimental sparse attention head (for running on datasets such as Pubmed)
# N.B. Because of limitations of current TF implementation, will work _only_ if batch_size = 1!
def sp_attn_head(seq, out_sz, adj_mat, activation, nb_nodes, in_drop=0.0, coef_drop=0.0, residual=False):
    with tf.name_scope('sp_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)

        f_1 = tf.reshape(f_1, (nb_nodes, 1))
        f_2 = tf.reshape(f_2, (nb_nodes, 1))

        f_1 = adj_mat*f_1
        f_2 = adj_mat * tf.transpose(f_2, [1,0])

        logits = tf.sparse_add(f_1, f_2)
        lrelu = tf.SparseTensor(indices=logits.indices, 
                values=tf.nn.leaky_relu(logits.values), 
                dense_shape=logits.dense_shape)
        coefs = tf.sparse_softmax(lrelu)

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

        # As tf.sparse_tensor_dense_matmul expects its arguments to have rank-2,
        # here we make an assumption that our input is of batch size 1, and reshape appropriately.
        # The method will fail in all other cases!
        coefs = tf.sparse_reshape(coefs, [nb_nodes, nb_nodes])
        seq_fts = tf.squeeze(seq_fts)
        vals = tf.sparse_tensor_dense_matmul(coefs, seq_fts)
        vals = tf.expand_dims(vals, axis=0)
        vals.set_shape([1, nb_nodes, out_sz])
        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

相应的位置都要使用稀疏的方式。