wehub-resource-sync
114 lines
3.7 KiB
Python
114 lines
3.7 KiB
Python
"""MXNet Module for APPNPConv"""
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# pylint: disable= no-member, arguments-differ, invalid-name
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import mxnet as mx
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from mxnet import nd
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from mxnet.gluon import nn
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from .... import function as fn
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class APPNPConv(nn.Block):
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r"""Approximate Personalized Propagation of Neural Predictions layer from `Predict then
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Propagate: Graph Neural Networks meet Personalized PageRank
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<https://arxiv.org/pdf/1810.05997.pdf>`__
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.. math::
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H^{0} &= X
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H^{l+1} &= (1-\alpha)\left(\tilde{D}^{-1/2}
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\tilde{A} \tilde{D}^{-1/2} H^{l}\right) + \alpha H^{0}
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where :math:`\tilde{A}` is :math:`A` + :math:`I`.
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Parameters
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----------
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k : int
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The number of iterations :math:`K`.
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alpha : float
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The teleport probability :math:`\alpha`.
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edge_drop : float, optional
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The dropout rate on edges that controls the
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messages received by each node. Default: ``0``.
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Example
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-------
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>>> import dgl
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>>> import numpy as np
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>>> import mxnet as mx
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>>> from dgl.nn import APPNPConv
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>>>
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>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
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>>> feat = mx.nd.ones((6, 10))
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>>> conv = APPNPConv(k=3, alpha=0.5)
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>>> conv.initialize(ctx=mx.cpu(0))
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>>> res = conv(g, feat)
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>>> res
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[[1. 1. 1. 1. 1. 1.
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1. 1. 1. 1. ]
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[1. 1. 1. 1. 1. 1.
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1. 1. 1. 1. ]
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[1. 1. 1. 1. 1. 1.
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1. 1. 1. 1. ]
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[1.0303301 1.0303301 1.0303301 1.0303301 1.0303301 1.0303301
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1.0303301 1.0303301 1.0303301 1.0303301 ]
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[0.86427665 0.86427665 0.86427665 0.86427665 0.86427665 0.86427665
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0.86427665 0.86427665 0.86427665 0.86427665]
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[0.5 0.5 0.5 0.5 0.5 0.5
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0.5 0.5 0.5 0.5 ]]
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<NDArray 6x10 @cpu(0)>
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"""
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def __init__(self, k, alpha, edge_drop=0.0):
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super(APPNPConv, self).__init__()
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self._k = k
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self._alpha = alpha
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with self.name_scope():
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self.edge_drop = nn.Dropout(edge_drop)
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def forward(self, graph, feat):
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r"""
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Description
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-----------
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Compute APPNP layer.
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Parameters
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----------
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graph : DGLGraph
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The graph.
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feat : mx.NDArray
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The input feature of shape :math:`(N, *)`. :math:`N` is the
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number of nodes, and :math:`*` could be of any shape.
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Returns
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-------
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mx.NDArray
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The output feature of shape :math:`(N, *)` where :math:`*`
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should be the same as input shape.
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"""
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with graph.local_scope():
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norm = mx.nd.power(
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mx.nd.clip(
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graph.in_degrees().astype(feat.dtype),
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a_min=1,
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a_max=float("inf"),
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),
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-0.5,
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)
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shp = norm.shape + (1,) * (feat.ndim - 1)
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norm = norm.reshape(shp).as_in_context(feat.context)
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feat_0 = feat
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for _ in range(self._k):
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# normalization by src node
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feat = feat * norm
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graph.ndata["h"] = feat
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graph.edata["w"] = self.edge_drop(
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nd.ones((graph.num_edges(), 1), ctx=feat.context)
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)
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graph.update_all(fn.u_mul_e("h", "w", "m"), fn.sum("m", "h"))
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feat = graph.ndata.pop("h")
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# normalization by dst node
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feat = feat * norm
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feat = (1 - self._alpha) * feat + self._alpha * feat_0
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return feat
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