import scipy.sparse
from sklearn.decomposition import TruncatedSVD
from sklearn.metrics import roc_auc_score, f1_score
import torch
import torch.nn.functional as F
from torch_sparse import coalesce
from torch_geometric.nn import SignedConv
from torch_geometric.utils import (negative_sampling,
structured_negative_sampling)
class SignedGCN(torch.nn.Module):
r"""The signed graph convolutional network model from the `"Signed Graph
Convolutional Network" <https://arxiv.org/abs/1808.06354>`_ paper.
Internally, this module uses the
:class:`torch_geometric.nn.conv.SignedConv` operator.
Args:
in_channels (int): Size of each input sample.
hidden_channels (int): Size of each hidden sample.
num_layers (int): Number of layers.
lamb (float, optional): Balances the contributions of the overall
objective. (default: :obj:`5`)
bias (bool, optional): If set to :obj:`False`, all layers will not
learn an additive bias. (default: :obj:`True`)
"""
def __init__(self, in_channels, hidden_channels, num_layers, lamb=5,
bias=True):
super(SignedGCN, self).__init__()
self.in_channels = in_channels
self.hidden_channels = hidden_channels
self.num_layers = num_layers
self.lamb = lamb
self.conv1 = SignedConv(in_channels, hidden_channels // 2,
first_aggr=True)
self.convs = torch.nn.ModuleList()
for i in range(num_layers - 1):
self.convs.append(
SignedConv(hidden_channels // 2, hidden_channels // 2,
first_aggr=False))
self.lin = torch.nn.Linear(2 * hidden_channels, 3)
self.reset_parameters()
def reset_parameters(self):
self.conv1.reset_parameters()
for conv in self.convs:
conv.reset_parameters()
self.lin.reset_parameters()
def split_edges(self, edge_index, test_ratio=0.2):
r"""Splits the edges :obj:`edge_index` into train and test edges.
Args:
edge_index (LongTensor): The edge indices.
test_ratio (float, optional): The ratio of test edges.
(default: :obj:`0.2`)
"""
mask = torch.ones(edge_index.size(1), dtype=torch.bool)
mask[torch.randperm(mask.size(0))[:int(test_ratio * mask.size(0))]] = 0
train_edge_index = edge_index[:, mask]
test_edge_index = edge_index[:, ~mask]
return train_edge_index, test_edge_index
def create_spectral_features(self, pos_edge_index, neg_edge_index,
num_nodes=None):
r"""Creates :obj:`in_channels` spectral node features based on
positive and negative edges.
Args:
pos_edge_index (LongTensor): The positive edge indices.
neg_edge_index (LongTensor): The negative edge indices.
num_nodes (int, optional): The number of nodes, *i.e.*
:obj:`max_val + 1` of :attr:`pos_edge_index` and
:attr:`neg_edge_index`. (default: :obj:`None`)
"""
edge_index = torch.cat([pos_edge_index, neg_edge_index], dim=1)
N = edge_index.max().item() + 1 if num_nodes is None else num_nodes
edge_index = edge_index.to(torch.device('cpu'))
pos_val = torch.full((pos_edge_index.size(1), ), 2, dtype=torch.float)
neg_val = torch.full((neg_edge_index.size(1), ), 0, dtype=torch.float)
val = torch.cat([pos_val, neg_val], dim=0)
row, col = edge_index
edge_index = torch.cat([edge_index, torch.stack([col, row])], dim=1)
val = torch.cat([val, val], dim=0)
edge_index, val = coalesce(edge_index, val, N, N)
val = val - 1
# Borrowed from:
# https://github.com/benedekrozemberczki/SGCN/blob/master/src/utils.py
edge_index = edge_index.detach().numpy()
val = val.detach().numpy()
A = scipy.sparse.coo_matrix((val, edge_index), shape=(N, N))
svd = TruncatedSVD(n_components=self.in_channels, n_iter=128)
svd.fit(A)
x = svd.components_.T
return torch.from_numpy(x).to(torch.float).to(pos_edge_index.device)
def forward(self, x, pos_edge_index, neg_edge_index):
"""Computes node embeddings :obj:`z` based on positive edges
:obj:`pos_edge_index` and negative edges :obj:`neg_edge_index`.
Args:
x (Tensor): The input node features.
pos_edge_index (LongTensor): The positive edge indices.
neg_edge_index (LongTensor): The negative edge indices.
"""
z = F.relu(self.conv1(x, pos_edge_index, neg_edge_index))
for conv in self.convs:
z = F.relu(conv(z, pos_edge_index, neg_edge_index))
return z
def discriminate(self, z, edge_index):
"""Given node embeddings :obj:`z`, classifies the link relation
between node pairs :obj:`edge_index` to be either positive,
negative or non-existent.
Args:
x (Tensor): The input node features.
edge_index (LongTensor): The edge indices.
"""
value = torch.cat([z[edge_index[0]], z[edge_index[1]]], dim=1)
value = self.lin(value)
return torch.log_softmax(value, dim=1)
def nll_loss(self, z, pos_edge_index, neg_edge_index):
"""Computes the discriminator loss based on node embeddings :obj:`z`,
and positive edges :obj:`pos_edge_index` and negative nedges
:obj:`neg_edge_index`.
Args:
z (Tensor): The node embeddings.
pos_edge_index (LongTensor): The positive edge indices.
neg_edge_index (LongTensor): The negative edge indices.
"""
edge_index = torch.cat([pos_edge_index, neg_edge_index], dim=1)
none_edge_index = negative_sampling(edge_index, z.size(0))
nll_loss = 0
nll_loss += F.nll_loss(
self.discriminate(z, pos_edge_index),
pos_edge_index.new_full((pos_edge_index.size(1), ), 0))
nll_loss += F.nll_loss(
self.discriminate(z, neg_edge_index),
neg_edge_index.new_full((neg_edge_index.size(1), ), 1))
nll_loss += F.nll_loss(
self.discriminate(z, none_edge_index),
none_edge_index.new_full((none_edge_index.size(1), ), 2))
return nll_loss / 3.0
def pos_embedding_loss(self, z, pos_edge_index):
"""Computes the triplet loss between positive node pairs and sampled
non-node pairs.
Args:
z (Tensor): The node embeddings.
pos_edge_index (LongTensor): The positive edge indices.
"""
i, j, k = structured_negative_sampling(pos_edge_index, z.size(0))
out = (z[i] - z[j]).pow(2).sum(dim=1) - (z[i] - z[k]).pow(2).sum(dim=1)
return torch.clamp(out, min=0).mean()
def neg_embedding_loss(self, z, neg_edge_index):
"""Computes the triplet loss between negative node pairs and sampled
non-node pairs.
Args:
z (Tensor): The node embeddings.
neg_edge_index (LongTensor): The negative edge indices.
"""
i, j, k = structured_negative_sampling(neg_edge_index, z.size(0))
out = (z[i] - z[k]).pow(2).sum(dim=1) - (z[i] - z[j]).pow(2).sum(dim=1)
return torch.clamp(out, min=0).mean()
def loss(self, z, pos_edge_index, neg_edge_index):
"""Computes the overall objective.
Args:
z (Tensor): The node embeddings.
pos_edge_index (LongTensor): The positive edge indices.
neg_edge_index (LongTensor): The negative edge indices.
"""
nll_loss = self.nll_loss(z, pos_edge_index, neg_edge_index)
loss_1 = self.pos_embedding_loss(z, pos_edge_index)
loss_2 = self.neg_embedding_loss(z, neg_edge_index)
return nll_loss + self.lamb * (loss_1 + loss_2)
def test(self, z, pos_edge_index, neg_edge_index):
"""Evaluates node embeddings :obj:`z` on positive and negative test
edges by computing AUC and F1 scores.
Args:
z (Tensor): The node embeddings.
pos_edge_index (LongTensor): The positive edge indices.
neg_edge_index (LongTensor): The negative edge indices.
"""
with torch.no_grad():
pos_p = self.discriminate(z, pos_edge_index)[:, :2].max(dim=1)[1]
neg_p = self.discriminate(z, neg_edge_index)[:, :2].max(dim=1)[1]
pred = (1 - torch.cat([pos_p, neg_p])).cpu()
y = torch.cat(
[pred.new_ones((pos_p.size(0))),
pred.new_zeros(neg_p.size(0))])
pred, y = pred.numpy(), y.numpy()
auc = roc_auc_score(y, pred)
f1 = f1_score(y, pred, average='binary') if pred.sum() > 0 else 0
return auc, f1
def __repr__(self):
return '{}({}, {}, num_layers={})'.format(self.__class__.__name__,
self.in_channels,
self.hidden_channels,
self.num_layers)
