图神经网络_06-基于图神经网络的图表征学习方法

基于图神经网络的图表征学习方法

图表征学习要求根据节点属性、边和边的属性(如果存在)生成一个向量作为图的表征,基于图表征可以做图的预测。基于图同构网络GIN(Graph Isomorphism Network)的图表征网络是当前最经典的图表征学习网络。

基于图同构网络(GIN)的图表征网络的实现过程

基于图同构网络的图表征学习主要包含以下两个过程:

  1. 首先计算得到节点表征;
  2. 对图上各个节点的表征做图池化(Graph Pooling),或者称为图读出(Graph Readout),得到图的表征(Graph Representation)。

基于图同构网络的图表征模块(GINGraphRepr Module)

首先采用GINNodeEmbedding模块对图上每一个节点做节点嵌入(Node Embedding),得到节点表征;然后对节点表征做图池化得到图的表征;
最后用一层线性变换对图表征转换为对图的预测。
代码如下:

import torch
from torch import nn
from torch_geometric.nn import global_add_pool, global_mean_pool, global_max_pool, GlobalAttention, Set2Set
from gin_node import GINNodeEmbedding

class GINGraphRepr(nn.Module):

    def __init__(self, num_tasks=1, num_layers=5, emb_dim=300, residual=False, drop_ratio=0, JK="last", graph_pooling="sum"):
        """GIN Graph Pooling Module
        Args:
            num_tasks (int, optional): number of labels to be predicted. Defaults to 1 (控制了图表征的维度,dimension of graph representation).
            num_layers (int, optional): number of GINConv layers. Defaults to 5.
            emb_dim (int, optional): dimension of node embedding. Defaults to 300.
            residual (bool, optional): adding residual connection or not. Defaults to False.
            drop_ratio (float, optional): dropout rate. Defaults to 0.
            JK (str, optional): 可选的值为"last"和"sum"。选"last",只取最后一层的结点的嵌入,选"sum"对各层的结点的嵌入求和。Defaults to "last".
            graph_pooling (str, optional): pooling method of node embedding. 可选的值为"sum","mean","max","attention"和"set2set"。 Defaults to "sum".

        Out:
            graph representation
        """
        super(GINGraphPooling, self).__init__()

        self.num_layers = num_layers
        self.drop_ratio = drop_ratio
        self.JK = JK
        self.emb_dim = emb_dim
        self.num_tasks = num_tasks

        if self.num_layers < 2:
            raise ValueError("Number of GNN layers must be greater than 1.")

        self.gnn_node = GINNodeEmbedding(num_layers, emb_dim, JK=JK, drop_ratio=drop_ratio, residual=residual)

        # Pooling function to generate whole-graph embeddings
        if graph_pooling == "sum":
            self.pool = global_add_pool
        elif graph_pooling == "mean":
            self.pool = global_mean_pool
        elif graph_pooling == "max":
            self.pool = global_max_pool
        elif graph_pooling == "attention":
            self.pool = GlobalAttention(gate_nn=nn.Sequential(
                nn.Linear(emb_dim, emb_dim), nn.BatchNorm1d(emb_dim), nn.ReLU(), nn.Linear(emb_dim, 1)))
        elif graph_pooling == "set2set":
            self.pool = Set2Set(emb_dim, processing_steps=2)
        else:
            raise ValueError("Invalid graph pooling type.")

        if graph_pooling == "set2set":
            self.graph_pred_linear = nn.Linear(2*self.emb_dim, self.num_tasks)
        else:
            self.graph_pred_linear = nn.Linear(self.emb_dim, self.num_tasks)

    def forward(self, batched_data):
        h_node = self.gnn_node(batched_data)

        h_graph = self.pool(h_node, batched_data.batch)
        output = self.graph_pred_linear(h_graph)

        if self.training:
            return output
        else:
            # At inference time, relu is applied to output to ensure positivity
            # 因为预测目标的取值范围就在 (0, 50] 内
            return torch.clamp(output, min=0, max=50)

以上可以看出,基于结点表征计算得到图表征的方法有:

  1. “sum”:对节点表征求和(torch_geometric.nn.glob.global_add_pool)。
  2. “mean”:对节点表征求平均(torch_geometric.nn.glob.global_mean_pool)。
  3. “max”:取节点表征的最大值。 对一个batch中所有节点计算节点表征各个维度的最大值(torch_geometric.nn.glob.global_max_pool)。
  4. “attention”:基于Attention对节点表征加权求和(torch_geometric.nn.glob.GlobalAttention);
    来自论文 “Gated Graph Sequence Neural Networks”
  5. “set2set”: 另一种基于Attention对节点表征加权求和的方法(torch_geometric.nn.glob.Set2Set)
    来自论文 “Order Matters: Sequence to sequence for sets”

基于图同构网络的节点嵌入模块(GINNodeEmbedding Module)

节点嵌入模块基于多层GINConv实现结点嵌入的计算。我们先忽略GINConv的实现。输入到此节点嵌入模块的节点属性为类别型向量,首先用AtomEncoder对其做嵌入得到第0层节点表征。然后逐层计算节点表征,从第1层开始到第num_layers层,每一层节点表征的计算都以上一层的节点表征h_list[layer]、边edge_index和边的属性edge_attr为输入。GINConv的层数越多,此节点嵌入模块的感受野(receptive field)越大,结点i的表征最远能捕获到结点i的距离为num_layers的邻接节点的信息。

import torch
from mol_encoder import AtomEncoder
from gin_conv import GINConv
import torch.nn.functional as F

# GNN to generate node embedding
class GINNodeEmbedding(torch.nn.Module):
    """
    Output:
        node representations
    """

    def __init__(self, num_layers, emb_dim, drop_ratio=0.5, JK="last", residual=False):
        """GIN Node Embedding Module"""

        super(GINNodeEmbedding, self).__init__()
        self.num_layers = num_layers
        self.drop_ratio = drop_ratio
        self.JK = JK
        # add residual connection or not
        self.residual = residual

        if self.num_layers < 2:
            raise ValueError("Number of GNN layers must be greater than 1.")

        self.atom_encoder = AtomEncoder(emb_dim)

        # List of GNNs
        self.convs = torch.nn.ModuleList()
        self.batch_norms = torch.nn.ModuleList()

        for layer in range(num_layers):
            self.convs.append(GINConv(emb_dim))
            self.batch_norms.append(torch.nn.BatchNorm1d(emb_dim))

    def forward(self, batched_data):
        x, edge_index, edge_attr = batched_data.x, batched_data.edge_index, batched_data.edge_attr

        # computing input node embedding
        h_list = [self.atom_encoder(x)]  # 先将类别型原子属性转化为原子表征
        for layer in range(self.num_layers):
            h = self.convs[layer](h_list[layer], edge_index, edge_attr)
            h = self.batch_norms[layer](h)
            if layer == self.num_layers - 1:
                # remove relu for the last layer
                h = F.dropout(h, self.drop_ratio, training=self.training)
            else:
                h = F.dropout(F.relu(h), self.drop_ratio, training=self.training)

            if self.residual:
                h += h_list[layer]

            h_list.append(h)

        # Different implementations of Jk-concat
        if self.JK == "last":
            node_representation = h_list[-1]
        elif self.JK == "sum":
            node_representation = 0
            for layer in range(self.num_layers + 1):
                node_representation += h_list[layer]

        return node_representation

GINConv–图同构卷积层

图同构卷积层的数学定义如下:
x i ′ = h Θ ( ( 1 + ϵ ) ⋅ x i + ∑ j ∈ N ( i ) x j ) \mathbf{x}^{\prime}_i = h_{\mathbf{\Theta}} \left( (1 + \epsilon) \cdot \mathbf{x}_i + \sum_{j \in \mathcal{N}(i)} \mathbf{x}_j \right) xi=hΘ(1+ϵ)xi+jN(i)xj
通过torch_geometric.nn.GINConv来使用图同构卷积层,然而该实现不支持存在边属性的图。这里我们自定义一个支持边属性的GINConv模块。

由于输入的边属性为类别型,我们需要先将类别型边属性转换为边表征。自定义的GINConv模块遵循“消息传递、消息聚合、消息更新”这一过程。

import torch
from torch import nn
from torch_geometric.nn import MessagePassing
import torch.nn.functional as F
from ogb.graphproppred.mol_encoder import BondEncoder


### GIN convolution along the graph structure
class GINConv(MessagePassing):
    def __init__(self, emb_dim):
        '''
            emb_dim (int): node embedding dimensionality
        '''
        super(GINConv, self).__init__(aggr = "add")

        self.mlp = nn.Sequential(nn.Linear(emb_dim, emb_dim), nn.BatchNorm1d(emb_dim), nn.ReLU(), nn.Linear(emb_dim, emb_dim))
        self.eps = nn.Parameter(torch.Tensor([0]))
        self.bond_encoder = BondEncoder(emb_dim = emb_dim)

    def forward(self, x, edge_index, edge_attr):
        edge_embedding = self.bond_encoder(edge_attr) # 先将类别型边属性转换为边表征
        out = self.mlp((1 + self.eps) *x + self.propagate(edge_index, x=x, edge_attr=edge_embedding))
        return out

    def message(self, x_j, edge_attr):
        return F.relu(x_j + edge_attr)
        
    def update(self, aggr_out):
        return aggr_out

AtomEncoder与 BondEncoder

在当前的例子中,节点(原子)和边(化学键)的属性都为离散值,属于不同的空间,无法直接融合在一起。通过嵌入(Embedding),我们可以将节点属性和边属性分别映射到一个新的空间,在这个新的空间中,我们就可以对节点和边进行信息融合。在GINConv中,message()函数中的x_j + edge_attr 操作执行了节点信息和边信息的融合。

import torch
from ogb.utils.features import get_atom_feature_dims, get_bond_feature_dims 

full_atom_feature_dims = get_atom_feature_dims()
full_bond_feature_dims = get_bond_feature_dims()

class AtomEncoder(torch.nn.Module):

    def __init__(self, emb_dim):
        super(AtomEncoder, self).__init__()
        
        self.atom_embedding_list = torch.nn.ModuleList()

        for i, dim in enumerate(full_atom_feature_dims):
            emb = torch.nn.Embedding(dim, emb_dim)
            torch.nn.init.xavier_uniform_(emb.weight.data)
            self.atom_embedding_list.append(emb)

    def forward(self, x):
        x_embedding = 0
        for i in range(x.shape[1]):
            x_embedding += self.atom_embedding_list[i](x[:,i])

        return x_embedding
class BondEncoder(torch.nn.Module):
    
    def __init__(self, emb_dim):
        super(BondEncoder, self).__init__()
        
        self.bond_embedding_list = torch.nn.ModuleList()

        for i, dim in enumerate(full_bond_feature_dims):
            emb = torch.nn.Embedding(dim, emb_dim)
            torch.nn.init.xavier_uniform_(emb.weight.data)
            self.bond_embedding_list.append(emb)

    def forward(self, edge_attr):
        bond_embedding = 0
        for i in range(edge_attr.shape[1]):
            bond_embedding += self.bond_embedding_list[i](edge_attr[:,i])

        return bond_embedding   
if __name__ == '__main__':
    from loader import GraphClassificationPygDataset
    dataset = GraphClassificationPygDataset(name = 'tox21')
    atom_enc = AtomEncoder(100)
    bond_enc = BondEncoder(100)

    print(atom_enc(dataset[0].x))
    print(bond_enc(dataset[0].edge_attr))

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