from torch_geometric.nn.conv import MessagePassing, GCNConv
[docs]class APPNP(MessagePassing):
r"""The approximate personalized propagation of neural predictions layer
from the `"Predict then Propagate: Graph Neural Networks meet Personalized
PageRank" <https://arxiv.org/abs/1810.05997>`_ paper
.. math::
\mathbf{X}^{(0)} &= \mathbf{X}
\mathbf{X}^{(k)} &= (1 - \alpha) \mathbf{\hat{D}}^{-1/2}
\mathbf{\hat{A}} \mathbf{\hat{D}}^{-1/2} \mathbf{X}^{(k-1)} + \alpha
\mathbf{X}^{(0)}
\mathbf{X}^{\prime} &= \mathbf{X}^{(K)},
where :math:`\mathbf{\hat{A}} = \mathbf{A} + \mathbf{I}` denotes the
adjacency matrix with inserted self-loops and
:math:`\hat{D}_{ii} = \sum_{j=0} \hat{A}_{ij}` its diagonal degree matrix.
Args:
K (int): Number of iterations :math:`K`.
alpha (float): Teleport probability :math:`\alpha`.
bias (bool, optional): If set to :obj:`False`, the layer will not learn
an additive bias. (default: :obj:`True`)
**kwargs (optional): Additional arguments of
:class:`torch_geometric.nn.conv.MessagePassing`.
"""
def __init__(self, K, alpha, bias=True, **kwargs):
super(APPNP, self).__init__(aggr='add', **kwargs)
self.K = K
self.alpha = alpha
[docs] def forward(self, x, edge_index, edge_weight=None):
""""""
edge_index, norm = GCNConv.norm(edge_index, x.size(self.node_dim),
edge_weight, dtype=x.dtype)
hidden = x
for k in range(self.K):
x = self.propagate(edge_index, x=x, norm=norm)
x = x * (1 - self.alpha)
x = x + self.alpha * hidden
return x
def message(self, x_j, norm):
return norm.view(-1, 1) * x_j
def __repr__(self):
return '{}(K={}, alpha={})'.format(self.__class__.__name__, self.K,
self.alpha)