"""MXNet Module for APPNPConv"""
# pylint: disable= no-member, arguments-differ, invalid-name
import mxnet as mx
from mxnet import nd
from mxnet.gluon import nn
from .... import function as fn
[docs]class APPNPConv(nn.Block):
r"""
Description
-----------
Approximate Personalized Propagation of Neural Predictions
layer from paper `Predict then Propagate: Graph Neural Networks
meet Personalized PageRank <https://arxiv.org/pdf/1810.05997.pdf>`__.
.. math::
H^{0} &= X
H^{l+1} &= (1-\alpha)\left(\tilde{D}^{-1/2}
\tilde{A} \tilde{D}^{-1/2} H^{l}\right) + \alpha H^{0}
where :math:`\tilde{A}` is :math:`A` + :math:`I`.
Parameters
----------
k : int
The number of iterations :math:`K`.
alpha : float
The teleport probability :math:`\alpha`.
edge_drop : float, optional
The dropout rate on edges that controls the
messages received by each node. Default: ``0``.
Example
-------
>>> import dgl
>>> import numpy as np
>>> import mxnet as mx
>>> from dgl.nn import APPNPConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = mx.nd.ones((6, 10))
>>> conv = APPNPConv(k=3, alpha=0.5)
>>> conv.initialize(ctx=mx.cpu(0))
>>> res = conv(g, feat)
>>> res
[[1. 1. 1. 1. 1. 1.
1. 1. 1. 1. ]
[1. 1. 1. 1. 1. 1.
1. 1. 1. 1. ]
[1. 1. 1. 1. 1. 1.
1. 1. 1. 1. ]
[1.0303301 1.0303301 1.0303301 1.0303301 1.0303301 1.0303301
1.0303301 1.0303301 1.0303301 1.0303301 ]
[0.86427665 0.86427665 0.86427665 0.86427665 0.86427665 0.86427665
0.86427665 0.86427665 0.86427665 0.86427665]
[0.5 0.5 0.5 0.5 0.5 0.5
0.5 0.5 0.5 0.5 ]]
<NDArray 6x10 @cpu(0)>
"""
def __init__(self,
k,
alpha,
edge_drop=0.):
super(APPNPConv, self).__init__()
self._k = k
self._alpha = alpha
with self.name_scope():
self.edge_drop = nn.Dropout(edge_drop)
[docs] def forward(self, graph, feat):
r"""
Description
-----------
Compute APPNP layer.
Parameters
----------
graph : DGLGraph
The graph.
feat : mx.NDArray
The input feature of shape :math:`(N, *)`. :math:`N` is the
number of nodes, and :math:`*` could be of any shape.
Returns
-------
mx.NDArray
The output feature of shape :math:`(N, *)` where :math:`*`
should be the same as input shape.
"""
with graph.local_scope():
norm = mx.nd.power(mx.nd.clip(
graph.in_degrees().astype(feat.dtype), a_min=1, a_max=float("inf")), -0.5)
shp = norm.shape + (1,) * (feat.ndim - 1)
norm = norm.reshape(shp).as_in_context(feat.context)
feat_0 = feat
for _ in range(self._k):
# normalization by src node
feat = feat * norm
graph.ndata['h'] = feat
graph.edata['w'] = self.edge_drop(
nd.ones((graph.number_of_edges(), 1), ctx=feat.context))
graph.update_all(fn.u_mul_e('h', 'w', 'm'),
fn.sum('m', 'h'))
feat = graph.ndata.pop('h')
# normalization by dst node
feat = feat * norm
feat = (1 - self._alpha) * feat + self._alpha * feat_0
return feat