"""Torch Module for Principal Neighbourhood Aggregation Convolution Layer"""
# pylint: disable= no-member, arguments-differ, invalid-name
import numpy as np
import torch
import torch.nn as nn
def aggregate_mean(h):
"""mean aggregation"""
return torch.mean(h, dim=1)
def aggregate_max(h):
"""max aggregation"""
return torch.max(h, dim=1)[0]
def aggregate_min(h):
"""min aggregation"""
return torch.min(h, dim=1)[0]
def aggregate_sum(h):
"""sum aggregation"""
return torch.sum(h, dim=1)
def aggregate_std(h):
"""standard deviation aggregation"""
return torch.sqrt(aggregate_var(h) + 1e-30)
def aggregate_var(h):
"""variance aggregation"""
h_mean_squares = torch.mean(h * h, dim=1)
h_mean = torch.mean(h, dim=1)
var = torch.relu(h_mean_squares - h_mean * h_mean)
return var
def _aggregate_moment(h, n):
"""moment aggregation: for each node (E[(X-E[X])^n])^{1/n}"""
h_mean = torch.mean(h, dim=1, keepdim=True)
h_n = torch.mean(torch.pow(h - h_mean, n), dim=1)
rooted_h_n = torch.sign(h_n) * torch.pow(torch.abs(h_n) + 1e-30, 1.0 / n)
return rooted_h_n
def aggregate_moment_3(h):
"""moment aggregation with n=3"""
return _aggregate_moment(h, n=3)
def aggregate_moment_4(h):
"""moment aggregation with n=4"""
return _aggregate_moment(h, n=4)
def aggregate_moment_5(h):
"""moment aggregation with n=5"""
return _aggregate_moment(h, n=5)
def scale_identity(h):
"""identity scaling (no scaling operation)"""
return h
def scale_amplification(h, D, delta):
"""amplification scaling"""
return h * (np.log(D + 1) / delta)
def scale_attenuation(h, D, delta):
"""attenuation scaling"""
return h * (delta / np.log(D + 1))
AGGREGATORS = {
"mean": aggregate_mean,
"sum": aggregate_sum,
"max": aggregate_max,
"min": aggregate_min,
"std": aggregate_std,
"var": aggregate_var,
"moment3": aggregate_moment_3,
"moment4": aggregate_moment_4,
"moment5": aggregate_moment_5,
}
SCALERS = {
"identity": scale_identity,
"amplification": scale_amplification,
"attenuation": scale_attenuation,
}
class PNAConvTower(nn.Module):
"""A single PNA tower in PNA layers"""
def __init__(
self,
in_size,
out_size,
aggregators,
scalers,
delta,
dropout=0.0,
edge_feat_size=0,
):
super(PNAConvTower, self).__init__()
self.in_size = in_size
self.out_size = out_size
self.aggregators = aggregators
self.scalers = scalers
self.delta = delta
self.edge_feat_size = edge_feat_size
self.M = nn.Linear(2 * in_size + edge_feat_size, in_size)
self.U = nn.Linear(
(len(aggregators) * len(scalers) + 1) * in_size, out_size
)
self.dropout = nn.Dropout(dropout)
self.batchnorm = nn.BatchNorm1d(out_size)
def reduce_func(self, nodes):
"""reduce function for PNA layer:
tensordot of multiple aggregation and scaling operations"""
msg = nodes.mailbox["msg"]
degree = msg.size(1)
h = torch.cat(
[AGGREGATORS[agg](msg) for agg in self.aggregators], dim=1
)
h = torch.cat(
[
SCALERS[scaler](h, D=degree, delta=self.delta)
if scaler != "identity"
else h
for scaler in self.scalers
],
dim=1,
)
return {"h_neigh": h}
def message(self, edges):
"""message function for PNA layer"""
if self.edge_feat_size > 0:
f = torch.cat(
[edges.src["h"], edges.dst["h"], edges.data["a"]], dim=-1
)
else:
f = torch.cat([edges.src["h"], edges.dst["h"]], dim=-1)
return {"msg": self.M(f)}
def forward(self, graph, node_feat, edge_feat=None):
"""compute the forward pass of a single tower in PNA convolution layer"""
# calculate graph normalization factors
snorm_n = torch.cat(
[
torch.ones(N, 1).to(node_feat) / N
for N in graph.batch_num_nodes()
],
dim=0,
).sqrt()
with graph.local_scope():
graph.ndata["h"] = node_feat
if self.edge_feat_size > 0:
assert edge_feat is not None, "Edge features must be provided."
graph.edata["a"] = edge_feat
graph.update_all(self.message, self.reduce_func)
h = self.U(torch.cat([node_feat, graph.ndata["h_neigh"]], dim=-1))
h = h * snorm_n
return self.dropout(self.batchnorm(h))
[docs]
class PNAConv(nn.Module):
r"""Principal Neighbourhood Aggregation Layer from `Principal Neighbourhood Aggregation
for Graph Nets <https://arxiv.org/abs/2004.05718>`__
A PNA layer is composed of multiple PNA towers. Each tower takes as input a split of the
input features, and computes the message passing as below.
.. math::
h_i^(l+1) = U(h_i^l, \oplus_{(i,j)\in E}M(h_i^l, e_{i,j}, h_j^l))
where :math:`h_i` and :math:`e_{i,j}` are node features and edge features, respectively.
:math:`M` and :math:`U` are MLPs, taking the concatenation of input for computing
output features. :math:`\oplus` represents the combination of various aggregators
and scalers. Aggregators aggregate messages from neighbours and scalers scale the
aggregated messages in different ways. :math:`\oplus` concatenates the output features
of each combination.
The output of multiple towers are concatenated and fed into a linear mixing layer for the
final output.
Parameters
----------
in_size : int
Input feature size; i.e. the size of :math:`h_i^l`.
out_size : int
Output feature size; i.e. the size of :math:`h_i^{l+1}`.
aggregators : list of str
List of aggregation function names(each aggregator specifies a way to aggregate
messages from neighbours), selected from:
* ``mean``: the mean of neighbour messages
* ``max``: the maximum of neighbour messages
* ``min``: the minimum of neighbour messages
* ``std``: the standard deviation of neighbour messages
* ``var``: the variance of neighbour messages
* ``sum``: the sum of neighbour messages
* ``moment3``, ``moment4``, ``moment5``: the normalized moments aggregation
:math:`(E[(X-E[X])^n])^{1/n}`
scalers: list of str
List of scaler function names, selected from:
* ``identity``: no scaling
* ``amplification``: multiply the aggregated message by :math:`\log(d+1)/\delta`,
where :math:`d` is the degree of the node.
* ``attenuation``: multiply the aggregated message by :math:`\delta/\log(d+1)`
delta: float
The degree-related normalization factor computed over the training set, used by scalers
for normalization. :math:`E[\log(d+1)]`, where :math:`d` is the degree for each node
in the training set.
dropout: float, optional
The dropout ratio. Default: 0.0.
num_towers: int, optional
The number of towers used. Default: 1. Note that in_size and out_size must be divisible
by num_towers.
edge_feat_size: int, optional
The edge feature size. Default: 0.
residual : bool, optional
The bool flag that determines whether to add a residual connection for the
output. Default: True. If in_size and out_size of the PNA conv layer are not
the same, this flag will be set as False forcibly.
Example
-------
>>> import dgl
>>> import torch as th
>>> from dgl.nn import PNAConv
>>>
>>> g = dgl.graph(([0,1,2,3,2,5], [1,2,3,4,0,3]))
>>> feat = th.ones(6, 10)
>>> conv = PNAConv(10, 10, ['mean', 'max', 'sum'], ['identity', 'amplification'], 2.5)
>>> ret = conv(g, feat)
"""
def __init__(
self,
in_size,
out_size,
aggregators,
scalers,
delta,
dropout=0.0,
num_towers=1,
edge_feat_size=0,
residual=True,
):
super(PNAConv, self).__init__()
self.in_size = in_size
self.out_size = out_size
assert (
in_size % num_towers == 0
), "in_size must be divisible by num_towers"
assert (
out_size % num_towers == 0
), "out_size must be divisible by num_towers"
self.tower_in_size = in_size // num_towers
self.tower_out_size = out_size // num_towers
self.edge_feat_size = edge_feat_size
self.residual = residual
if self.in_size != self.out_size:
self.residual = False
self.towers = nn.ModuleList(
[
PNAConvTower(
self.tower_in_size,
self.tower_out_size,
aggregators,
scalers,
delta,
dropout=dropout,
edge_feat_size=edge_feat_size,
)
for _ in range(num_towers)
]
)
self.mixing_layer = nn.Sequential(
nn.Linear(out_size, out_size), nn.LeakyReLU()
)
[docs]
def forward(self, graph, node_feat, edge_feat=None):
r"""
Description
-----------
Compute PNA layer.
Parameters
----------
graph : DGLGraph
The graph.
node_feat : torch.Tensor
The input feature of shape :math:`(N, h_n)`. :math:`N` is the number of
nodes, and :math:`h_n` must be the same as in_size.
edge_feat : torch.Tensor, optional
The edge feature of shape :math:`(M, h_e)`. :math:`M` is the number of
edges, and :math:`h_e` must be the same as edge_feat_size.
Returns
-------
torch.Tensor
The output node feature of shape :math:`(N, h_n')` where :math:`h_n'`
should be the same as out_size.
"""
h_cat = torch.cat(
[
tower(
graph,
node_feat[
:,
ti * self.tower_in_size : (ti + 1) * self.tower_in_size,
],
edge_feat,
)
for ti, tower in enumerate(self.towers)
],
dim=1,
)
h_out = self.mixing_layer(h_cat)
# add residual connection
if self.residual:
h_out = h_out + node_feat
return h_out