wehub-resource-sync
110 lines
3.6 KiB
Python
110 lines
3.6 KiB
Python
"""MXNet Module for DenseChebConv"""
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# pylint: disable= no-member, arguments-differ, invalid-name
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import math
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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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class DenseChebConv(nn.Block):
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r"""Chebyshev Spectral Graph Convolution layer from `Convolutional Neural Networks on Graphs
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with Fast Localized Spectral Filtering <https://arxiv.org/pdf/1606.09375.pdf>`__
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We recommend to use this module when applying ChebConv on dense graphs.
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Parameters
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----------
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in_feats: int
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Dimension of input features :math:`h_i^{(l)}`.
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out_feats: int
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Dimension of output features :math:`h_i^{(l+1)}`.
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k : int
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Chebyshev filter size.
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activation : function, optional
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Activation function, default is ReLu.
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bias : bool, optional
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If True, adds a learnable bias to the output. Default: ``True``.
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See also
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--------
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`ChebConv <https://docs.dgl.ai/api/python/nn.pytorch.html#chebconv>`__
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"""
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def __init__(self, in_feats, out_feats, k, bias=True):
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super(DenseChebConv, self).__init__()
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self._in_feats = in_feats
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self._out_feats = out_feats
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self._k = k
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with self.name_scope():
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self.fc = nn.Sequential()
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for _ in range(k):
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self.fc.add(
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nn.Dense(
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out_feats,
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in_units=in_feats,
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use_bias=False,
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weight_initializer=mx.init.Xavier(
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magnitude=math.sqrt(2.0)
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),
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)
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)
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if bias:
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self.bias = self.params.get(
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"bias", shape=(out_feats,), init=mx.init.Zero()
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)
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else:
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self.bias = None
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def forward(self, adj, feat, lambda_max=None):
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r"""
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Description
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-----------
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Compute (Dense) Chebyshev Spectral Graph Convolution layer.
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Parameters
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----------
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adj : mxnet.NDArray
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The adjacency matrix of the graph to apply Graph Convolution on,
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should be of shape :math:`(N, N)`, where a row represents the destination
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and a column represents the source.
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feat : mxnet.NDArray
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The input feature of shape :math:`(N, D_{in})` where :math:`D_{in}`
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is size of input feature, :math:`N` is the number of nodes.
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lambda_max : float or None, optional
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A float value indicates the largest eigenvalue of given graph.
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Default: None.
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Returns
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-------
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mxnet.NDArray
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The output feature of shape :math:`(N, D_{out})` where :math:`D_{out}`
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is size of output feature.
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"""
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A = adj.astype(feat.dtype).as_in_context(feat.context)
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num_nodes = A.shape[0]
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in_degree = 1.0 / nd.clip(A.sum(axis=1), 1, float("inf")).sqrt()
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D_invsqrt = nd.diag(in_degree)
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I = nd.eye(num_nodes, ctx=A.context)
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L = I - nd.dot(D_invsqrt, nd.dot(A, D_invsqrt))
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if lambda_max is None:
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# NOTE(zihao): this only works for directed graph.
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lambda_max = (nd.linalg.syevd(L)[1]).max()
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L_hat = 2 * L / lambda_max - I
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Z = [nd.eye(num_nodes, ctx=A.context)]
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Zh = self.fc[0](feat)
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for i in range(1, self._k):
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if i == 1:
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Z.append(L_hat)
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else:
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Z.append(2 * nd.dot(L_hat, Z[-1]) - Z[-2])
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Zh = Zh + nd.dot(Z[i], self.fc[i](feat))
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if self.bias is not None:
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Zh = Zh + self.bias.data(feat.context)
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return Zh
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