dgl version:0.5.x
說明： 在SAGEConv中，如果想要再消息傳遞過程中，使用邊上的信息，可以將fn.copy_src('h', 'm') 替換為 fn.copy_e('h', 'm')。
\[\begin{align}\begin{aligned}h_{\mathcal{N}(i)}^{(l+1)} &= \mathrm{aggregate} \left(\{h_{j}^{l}, \forall j \in \mathcal{N}(i) \}\right)\\h_{i}^{(l+1)} &= \sigma \left(W \cdot \mathrm{concat} (h_{i}^{l}, h_{\mathcal{N}(i)}^{l+1}) \right)\\h_{i}^{(l+1)} &= \mathrm{norm}(h_{i}^{l})\end{aligned}\end{align} \]
dgl SAGEConv 過程：
feat(ndim)為節點的特征，其中n為節點個數，dim為特征的維度
如果是同構圖：
conv = SAGEConv(dim,dim_out,'pool') 返回一個conv layer實例，
res = conv(g, feat) 在圖g上對feat進行SAGEConv操作，輸入的維度是dim，輸出的維度是dim_out，同構圖輸出和輸入的節點數相同，即res的維度是ndim_out
如果是二部圖：
conv = SAGEConv((dim_v,dim_u),dim_out,'pool')
res = conv(g, (feat_v,feat_u)) 輸入的維度是dim_v和dim_u,其中v當作源節點，U當作目標節點，輸出的維度是dim_out，二部圖輸出節點數與u的節點數相同，即res的維度是n_u*dim_out
消息傳遞階段，同構圖使用graph.number_of_dst_nodes()取出feat_src對應feat_dst
h_self = feat_dst # 將feat_dst 作為目的節點自身特征
graph.srcdata['h'] = feat_src
對不同的聚合方法使用不同的消息傳遞過程，
graph.update_all(fn.copy_src('h', 'm'), fn.mean('m', 'neigh')) # aggre_type == 'mean' ， fn.copy_src('h', 'm')是message_func將源節點的'h'傳遞到目的節點的'm'，fn.mean('m', 'neigh')是reduce_func對目的節點的消息'm'聚合到'neigh'
h_neigh = graph.dstdata['neigh']
這個時候h_self的維度和目的節點的特征維度相同，h_neigh的維度和目的節點的特征維度相同，需要進行線性變換將維度轉成dim_out
rst = self.fc_self(h_self) + self.fc_neigh(h_neigh)
"""Torch Module for GraphSAGE layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
import torch
from torch import nn
from torch.nn import functional as F
from .... import function as fn
from ....utils import expand_as_pair, check_eq_shape
class SAGEConv(nn.Module):
r"""
Description
-----------
GraphSAGE layer from paper `Inductive Representation Learning on
Large Graphs <https://arxiv.org/pdf/1706.02216.pdf>`__.
.. math::
h_{\mathcal{N}(i)}^{(l+1)} &= \mathrm{aggregate}
\left(\{h_{j}^{l}, \forall j \in \mathcal{N}(i) \}\right)
h_{i}^{(l+1)} &= \sigma \left(W \cdot \mathrm{concat}
(h_{i}^{l}, h_{\mathcal{N}(i)}^{l+1}) \right)
h_{i}^{(l+1)} &= \mathrm{norm}(h_{i}^{l})
Parameters
----------
in_feats : int, or pair of ints
Input feature size; i.e, the number of dimensions of :math:`h_i^{(l)}`.
GATConv can be applied on homogeneous graph and unidirectional
`bipartite graph <https://docs.dgl.ai/generated/dgl.bipartite.html?highlight=bipartite>`__.
If the layer applies on a unidirectional bipartite graph, ``in_feats``
specifies the input feature size on both the source and destination nodes. If
a scalar is given, the source and destination node feature size would take the
same value.
If aggregator type is ``gcn``, the feature size of source and destination nodes
are required to be the same.
out_feats : int
Output feature size; i.e, the number of dimensions of :math:`h_i^{(l+1)}`.
feat_drop : float
Dropout rate on features, default: ``0``.
aggregator_type : str
Aggregator type to use (``mean``, ``gcn``, ``pool``, ``lstm``).
bias : bool
If True, adds a learnable bias to the output. Default: ``True``.
norm : callable activation function/layer or None, optional
If not None, applies normalization to the updated node features.
activation : callable activation function/layer or None, optional
If not None, applies an activation function to the updated node features.
Default: ``None``.
Examples
--------
>>> import dgl
>>> import numpy as np
>>> import torch as th
>>> from dgl.nn import SAGEConv
>>> # Case 1: Homogeneous graph
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> g = dgl.add_self_loop(g)
>>> feat = th.ones(6, 10)
>>> conv = SAGEConv(10, 2, 'pool')
>>> res = conv(g, feat)
>>> res
tensor([[-1.0888, -2.1099],
[-1.0888, -2.1099],
[-1.0888, -2.1099],
[-1.0888, -2.1099],
[-1.0888, -2.1099],
[-1.0888, -2.1099]], grad_fn=<AddBackward0>)
>>> # Case 2: Unidirectional bipartite graph
>>> u = [0, 1, 0, 0, 1]
>>> v = [0, 1, 2, 3, 2]
>>> g = dgl.bipartite((u, v))
>>> u_fea = th.rand(2, 5)
>>> v_fea = th.rand(4, 10)
>>> conv = SAGEConv((5, 10), 2, 'mean')
>>> res = conv(g, (u_fea, v_fea))
>>> res
tensor([[ 0.3163, 3.1166],
[ 0.3866, 2.5398],
[ 0.5873, 1.6597],
[-0.2502, 2.8068]], grad_fn=<AddBackward0>)
"""
def __init__(self,
in_feats,
out_feats,
aggregator_type,
feat_drop=0.,
bias=True,
norm=None,
activation=None):
super(SAGEConv, self).__init__()
# 將in_feats展成 in_src 和 in_dst 兩部分
self._in_src_feats, self._in_dst_feats = expand_as_pair(in_feats)
self._out_feats = out_feats
self._aggre_type = aggregator_type
self.norm = norm
self.feat_drop = nn.Dropout(feat_drop)
self.activation = activation
# aggregator type: mean/pool/lstm/gcn
if aggregator_type == 'pool':
self.fc_pool = nn.Linear(self._in_src_feats, self._in_src_feats)
if aggregator_type == 'lstm':
self.lstm = nn.LSTM(self._in_src_feats, self._in_src_feats, batch_first=True)
if aggregator_type != 'gcn':
self.fc_self = nn.Linear(self._in_dst_feats, out_feats, bias=bias)
# 線性變換，維度變為out_feats
self.fc_neigh = nn.Linear(self._in_src_feats, out_feats, bias=bias)
self.reset_parameters()
def reset_parameters(self):
r"""
Description
-----------
Reinitialize learnable parameters.
Note
----
The linear weights :math:`W^{(l)}` are initialized using Glorot uniform initialization.
The LSTM module is using xavier initialization method for its weights.
"""
gain = nn.init.calculate_gain('relu')
if self._aggre_type == 'pool':
nn.init.xavier_uniform_(self.fc_pool.weight, gain=gain)
if self._aggre_type == 'lstm':
self.lstm.reset_parameters()
if self._aggre_type != 'gcn':
nn.init.xavier_uniform_(self.fc_self.weight, gain=gain)
nn.init.xavier_uniform_(self.fc_neigh.weight, gain=gain)
def _lstm_reducer(self, nodes):
"""LSTM reducer
NOTE(zihao): lstm reducer with default schedule (degree bucketing)
is slow, we could accelerate this with degree padding in the future.
"""
m = nodes.mailbox['m'] # (B, L, D)
batch_size = m.shape[0]
h = (m.new_zeros((1, batch_size, self._in_src_feats)),
m.new_zeros((1, batch_size, self._in_src_feats)))
_, (rst, _) = self.lstm(m, h)
return {'neigh': rst.squeeze(0)}
def forward(self, graph, feat):
r"""
Description
-----------
Compute GraphSAGE layer.
Parameters
----------
graph : DGLGraph
The graph.
feat : torch.Tensor or pair of torch.Tensor
If a torch.Tensor is given, it represents the input feature of shape
:math:`(N, D_{in})`
where :math:`D_{in}` is size of input feature, :math:`N` is the number of nodes.
If a pair of torch.Tensor is given, the pair must contain two tensors of shape
:math:`(N_{in}, D_{in_{src}})` and :math:`(N_{out}, D_{in_{dst}})`.
Returns
-------
torch.Tensor
The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
is size of output feature.
"""
# 如果是同構圖，使用graph.number_of_dst_nodes()取出feat_src對應feat_dst
# 如果是二部圖， 直接獲取feat_src 和 feat_dst
with graph.local_scope():
if isinstance(feat, tuple):
feat_src = self.feat_drop(feat[0])
feat_dst = self.feat_drop(feat[1])
else:
feat_src = feat_dst = self.feat_drop(feat)
if graph.is_block:
feat_dst = feat_src[:graph.number_of_dst_nodes()]
# feat_dst 傳給h_self
h_self = feat_dst
# Handle the case of graphs without edges
if graph.number_of_edges() == 0:
graph.dstdata['neigh'] = torch.zeros(
feat_dst.shape[0], self._in_src_feats).to(feat_dst)
if self._aggre_type == 'mean':
graph.srcdata['h'] = feat_src
graph.update_all(fn.copy_src('h', 'm'), fn.mean('m', 'neigh'))
h_neigh = graph.dstdata['neigh']
elif self._aggre_type == 'gcn':
check_eq_shape(feat)
graph.srcdata['h'] = feat_src
graph.dstdata['h'] = feat_dst # same as above if homogeneous
graph.update_all(fn.copy_src('h', 'm'), fn.sum('m', 'neigh'))
# divide in_degrees
degs = graph.in_degrees().to(feat_dst)
h_neigh = (graph.dstdata['neigh'] + graph.dstdata['h']) / (degs.unsqueeze(-1) + 1)
elif self._aggre_type == 'pool':
graph.srcdata['h'] = F.relu(self.fc_pool(feat_src))
graph.update_all(fn.copy_src('h', 'm'), fn.max('m', 'neigh'))
h_neigh = graph.dstdata['neigh']
elif self._aggre_type == 'lstm':
graph.srcdata['h'] = feat_src
graph.update_all(fn.copy_src('h', 'm'), self._lstm_reducer)
h_neigh = graph.dstdata['neigh']
else:
raise KeyError('Aggregator type {} not recognized.'.format(self._aggre_type))
# GraphSAGE GCN does not require fc_self.
if self._aggre_type == 'gcn':
rst = self.fc_neigh(h_neigh)
else:
rst = self.fc_self(h_self) + self.fc_neigh(h_neigh)
# activation
if self.activation is not None:
rst = self.activation(rst)
# normalization
if self.norm is not None:
rst = self.norm(rst)
return rst