https://www.bilibili.com/medialist/play/watchlater/BV18b4y1k7no
这个视频是讲怎么用代码把GCN的公式实现的

DGL

消息传递范式

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如何更新（t+1）时刻结点v的特征？ 假设v有邻居有u等结点，以下步骤以邻居u举例

  1. (t+1)时刻，收集 t时刻 结点u,v和边e（由uv构成）的特征
  2. 聚合v的所有邻居发送过来的消息，再加上v自身的特征。更新v

image.png
image.png

GraphConv

参数说明

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入度为0的情况下：
image.png只有bias，没有意义。
但是参数构造里可以选择是否允许。
（可以在构造图的时候加一个自环loof，避免入度为0的情况。仅限同构图。）
image.png

forward()函数

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image.png
把源节点的特征h 作为消息m存储在边上

image.png
h 乘以 edge_weight 存储在m

根据输入和输出特征的大小来选择计算量比较小的方式
image.png
例子

  1. import dgl
  2. import numpy as np
  3. import torch as th
  4. from dgl.nn import GraphConv
  1. # Case 1: 同构图
  2. g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
  3. g = dgl.add_self_loop(g)    #这里加了环
  4. feat = th.ones(6, 10)
  5. conv = GraphConv(10, 2, norm='both', weight=True, bias=True)
  6. res = conv(g, feat)
  7. print(res)
  9. #
  10. tensor([[ 1.3326, -0.2797],
  11.         [ 1.4673, -0.3080],
  12.         [ 1.3326, -0.2797],
  13.         [ 1.6871, -0.3541],
  14.         [ 1.7711, -0.3717],
  15.         [ 1.0375, -0.2178]], grad_fn=<AddBackward0>)
  17. # allow_zero_in_degree example 不加环的情况
  18. g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
  19. conv = GraphConv(10, 2, norm='both', weight=True, bias=True, allow_zero_in_degree=True)
  20. res = conv(g, feat)
  21. print(res)
  22. #
  23. tensor([[-0.2473, -0.4631],
  24.         [-0.3497, -0.6549],
  25.         [-0.3497, -0.6549],
  26.         [-0.4221, -0.7905],
  27.         [-0.3497, -0.6549],
  28.         [ 0.0000,  0.0000]], grad_fn=<AddBackward0>)

代码

删去注释后的实现代码，官方文档：https://docs.dgl.ai/_modules/dgl/nn/pytorch/conv/graphconv.html#GraphConv

  1. class GraphConv(nn.Module):
  3.     def __init__(self,
  4.                  in_feats,
  5.                  out_feats,
  6.                  norm='both',
  7.                  weight=True,
  8.                  bias=True,
  9.                  activation=None,
  10.                  allow_zero_in_degree=False):
  11.         super(GraphConv, self).__init__()
  12.         if norm not in ('none', 'both', 'right', 'left'):
  13.             raise DGLError('Invalid norm value. Must be either "none", "both", "right" or "left".'
  14.                            ' But got "{}".'.format(norm))
  15.         self._in_feats = in_feats
  16.         self._out_feats = out_feats
  17.         self._norm = norm
  18.         self._allow_zero_in_degree = allow_zero_in_degree
  20.         if weight:
  21.             self.weight = nn.Parameter(th.Tensor(in_feats, out_feats))
  22.         else:
  23.             self.register_parameter('weight', None)
  25.         if bias:
  26.             self.bias = nn.Parameter(th.Tensor(out_feats))
  27.         else:
  28.             self.register_parameter('bias', None)
  30.         self.reset_parameters()
  32.         self._activation = activation
  34.     def reset_parameters(self):
  36.         if self.weight is not None:
  37.             init.xavier_uniform_(self.weight)
  38.         if self.bias is not None:
  39.             init.zeros_(self.bias)
  42.     def set_allow_zero_in_degree(self, set_value):
  44.         self._allow_zero_in_degree = set_value
  47.    def forward(self, graph, feat, weight=None, edge_weight=None):
  49.         with graph.local_scope():
  50.             if not self._allow_zero_in_degree:
  51.                 if (graph.in_degrees() == 0).any():
  52.                     raise DGLError('There are 0-in-degree nodes in the graph, '
  53.                                    'output for those nodes will be invalid. '
  54.                                    'This is harmful for some applications, '
  55.                                    'causing silent performance regression. '
  56.                                    'Adding self-loop on the input graph by '
  57.                                    'calling `g = dgl.add_self_loop(g)` will resolve '
  58.                                    'the issue. Setting ``allow_zero_in_degree`` '
  59.                                    'to be `True` when constructing this module will '
  60.                                    'suppress the check and let the code run.')
  61.             aggregate_fn = fn.copy_src('h', 'm')
  62.             if edge_weight is not None:
  63.                 assert edge_weight.shape[0] == graph.number_of_edges()
  64.                 graph.edata['_edge_weight'] = edge_weight
  65.                 aggregate_fn = fn.u_mul_e('h', '_edge_weight', 'm')
  67.             # (BarclayII) For RGCN on heterogeneous graphs we need to support GCN on bipartite.
  68.             feat_src, feat_dst = expand_as_pair(feat, graph)
  69.             if self._norm in ['left', 'both']:
  70.                 degs = graph.out_degrees().float().clamp(min=1)
  71.                 if self._norm == 'both':
  72.                     norm = th.pow(degs, -0.5)
  73.                 else:
  74.                     norm = 1.0 / degs
  75.                 shp = norm.shape + (1,) * (feat_src.dim() - 1)
  76.                 norm = th.reshape(norm, shp)
  77.                 feat_src = feat_src * norm
  79.             if weight is not None:
  80.                 if self.weight is not None:
  81.                     raise DGLError('External weight is provided while at the same time the'
  82.                                    ' module has defined its own weight parameter. Please'
  83.                                    ' create the module with flag weight=False.')
  84.             else:
  85.                 weight = self.weight
  87.             if self._in_feats > self._out_feats:
  88.                 # mult W first to reduce the feature size for aggregation.
  89.                 if weight is not None:
  90.                     feat_src = th.matmul(feat_src, weight)
  91.                 graph.srcdata['h'] = feat_src
  92.                 graph.update_all(aggregate_fn, fn.sum(msg='m', out='h'))
  93.                 rst = graph.dstdata['h']
  94.             else:
  95.                 # aggregate first then mult W
  96.                 graph.srcdata['h'] = feat_src
  97.                 graph.update_all(aggregate_fn, fn.sum(msg='m', out='h'))
  98.                 rst = graph.dstdata['h']
  99.                 if weight is not None:
  100.                     rst = th.matmul(rst, weight)
  102.             if self._norm in ['right', 'both']:
  103.                 degs = graph.in_degrees().float().clamp(min=1)
  104.                 if self._norm == 'both':
  105.                     norm = th.pow(degs, -0.5)
  106.                 else:
  107.                     norm = 1.0 / degs
  108.                 shp = norm.shape + (1,) * (feat_dst.dim() - 1)
  109.                 norm = th.reshape(norm, shp)
  110.                 rst = rst * norm
  112.             if self.bias is not None:
  113.                 rst = rst + self.bias
  115.             if self._activation is not None:
  116.                 rst = self._activation(rst)
  118.             return rst
  121.     def extra_repr(self):
  123.         summary = 'in={_in_feats}, out={_out_feats}'
  124.         summary += ', normalization={_norm}'
  125.         if '_activation' in self.__dict__:
  126.             summary += ', activation={_activation}'
  127.         return summary.format(**self.__dict__)