"""
.. _model-rgcn:
Relational Graph Convolutional Network
================================================
**Author:** Lingfan Yu, Mufei Li, Zheng Zhang
.. warning::
The tutorial aims at gaining insights into the paper, with code as a mean
of explanation. The implementation thus is NOT optimized for running
efficiency. For recommended implementation, please refer to the `official
examples `_.
In this tutorial, you learn how to implement a relational graph convolutional
network (R-GCN). This type of network is one effort to generalize GCN
to handle different relationships between entities in a knowledge base. To
learn more about the research behind R-GCN, see `Modeling Relational Data with Graph Convolutional
Networks `_
The straightforward graph convolutional network (GCN) exploits
structural information of a dataset (that is, the graph connectivity) in order to
improve the extraction of node representations. Graph edges are left as
untyped.
A knowledge graph is made up of a collection of triples in the form
subject, relation, object. Edges thus encode important information and
have their own embeddings to be learned. Furthermore, there may exist
multiple edges among any given pair.
"""
###############################################################################
# A brief introduction to R-GCN
# ---------------------------
# In *statistical relational learning* (SRL), there are two fundamental
# tasks:
#
# - **Entity classification** - Where you assign types and categorical
# properties to entities.
# - **Link prediction** - Where you recover missing triples.
#
# In both cases, missing information is expected to be recovered from the
# neighborhood structure of the graph. For example, the R-GCN
# paper cited earlier provides the following example. Knowing that Mikhail Baryshnikov was educated at the Vaganova Academy
# implies both that Mikhail Baryshnikov should have the label person, and
# that the triple (Mikhail Baryshnikov, lived in, Russia) must belong to the
# knowledge graph.
#
# R-GCN solves these two problems using a common graph convolutional network. It's
# extended with multi-edge encoding to compute embedding of the entities, but
# with different downstream processing.
#
# - Entity classification is done by attaching a softmax classifier at the
# final embedding of an entity (node). Training is through loss of standard
# cross-entropy.
# - Link prediction is done by reconstructing an edge with an autoencoder
# architecture, using a parameterized score function. Training uses negative
# sampling.
#
# This tutorial focuses on the first task, entity classification, to show how to generate entity
# representation. `Complete
# code `_
# for both tasks is found in the DGL Github repository.
#
# Key ideas of R-GCN
# -------------------
# Recall that in GCN, the hidden representation for each node :math:`i` at
# :math:`(l+1)^{th}` layer is computed by:
#
# .. math:: h_i^{l+1} = \sigma\left(\sum_{j\in N_i}\frac{1}{c_i} W^{(l)} h_j^{(l)}\right)~~~~~~~~~~(1)\\
#
# where :math:`c_i` is a normalization constant.
#
# The key difference between R-GCN and GCN is that in R-GCN, edges can
# represent different relations. In GCN, weight :math:`W^{(l)}` in equation
# :math:`(1)` is shared by all edges in layer :math:`l`. In contrast, in
# R-GCN, different edge types use different weights and only edges of the
# same relation type :math:`r` are associated with the same projection weight
# :math:`W_r^{(l)}`.
#
# So the hidden representation of entities in :math:`(l+1)^{th}` layer in
# R-GCN can be formulated as the following equation:
#
# .. math:: h_i^{l+1} = \sigma\left(W_0^{(l)}h_i^{(l)}+\sum_{r\in R}\sum_{j\in N_i^r}\frac{1}{c_{i,r}}W_r^{(l)}h_j^{(l)}\right)~~~~~~~~~~(2)\\
#
# where :math:`N_i^r` denotes the set of neighbor indices of node :math:`i`
# under relation :math:`r\in R` and :math:`c_{i,r}` is a normalization
# constant. In entity classification, the R-GCN paper uses
# :math:`c_{i,r}=|N_i^r|`.
#
# The problem of applying the above equation directly is the rapid growth of
# the number of parameters, especially with highly multi-relational data. In
# order to reduce model parameter size and prevent overfitting, the original
# paper proposes to use basis decomposition.
#
# .. math:: W_r^{(l)}=\sum\limits_{b=1}^B a_{rb}^{(l)}V_b^{(l)}~~~~~~~~~~(3)\\
#
# Therefore, the weight :math:`W_r^{(l)}` is a linear combination of basis
# transformation :math:`V_b^{(l)}` with coefficients :math:`a_{rb}^{(l)}`.
# The number of bases :math:`B` is much smaller than the number of relations
# in the knowledge base.
#
# .. note::
# Another weight regularization, block-decomposition, is implemented in
# the `link prediction `_.
#
# Implement R-GCN in DGL
# ----------------------
#
# An R-GCN model is composed of several R-GCN layers. The first R-GCN layer
# also serves as input layer and takes in features (for example, description texts)
# that are associated with node entity and project to hidden space. In this tutorial,
# we only use the entity ID as an entity feature.
#
# R-GCN layers
# ~~~~~~~~~~~~
#
# For each node, an R-GCN layer performs the following steps:
#
# - Compute outgoing message using node representation and weight matrix
# associated with the edge type (message function)
# - Aggregate incoming messages and generate new node representations (reduce
# and apply function)
#
# The following code is the definition of an R-GCN hidden layer.
#
# .. note::
# Each relation type is associated with a different weight. Therefore,
# the full weight matrix has three dimensions: relation, input_feature,
# output_feature.
#
# .. note::
#
# This is showing how to implement an R-GCN from scratch. DGL provides a more
# efficient :class:`builtin R-GCN layer module `.
#
import torch
import torch.nn as nn
import torch.nn.functional as F
from dgl import DGLGraph
import dgl.function as fn
from functools import partial
class RGCNLayer(nn.Module):
def __init__(self, in_feat, out_feat, num_rels, num_bases=-1, bias=None,
activation=None, is_input_layer=False):
super(RGCNLayer, self).__init__()
self.in_feat = in_feat
self.out_feat = out_feat
self.num_rels = num_rels
self.num_bases = num_bases
self.bias = bias
self.activation = activation
self.is_input_layer = is_input_layer
# sanity check
if self.num_bases <= 0 or self.num_bases > self.num_rels:
self.num_bases = self.num_rels
# weight bases in equation (3)
self.weight = nn.Parameter(torch.Tensor(self.num_bases, self.in_feat,
self.out_feat))
if self.num_bases < self.num_rels:
# linear combination coefficients in equation (3)
self.w_comp = nn.Parameter(torch.Tensor(self.num_rels, self.num_bases))
# add bias
if self.bias:
self.bias = nn.Parameter(torch.Tensor(out_feat))
# init trainable parameters
nn.init.xavier_uniform_(self.weight,
gain=nn.init.calculate_gain('relu'))
if self.num_bases < self.num_rels:
nn.init.xavier_uniform_(self.w_comp,
gain=nn.init.calculate_gain('relu'))
if self.bias:
nn.init.xavier_uniform_(self.bias,
gain=nn.init.calculate_gain('relu'))
def forward(self, g):
if self.num_bases < self.num_rels:
# generate all weights from bases (equation (3))
weight = self.weight.view(self.in_feat, self.num_bases, self.out_feat)
weight = torch.matmul(self.w_comp, weight).view(self.num_rels,
self.in_feat, self.out_feat)
else:
weight = self.weight
if self.is_input_layer:
def message_func(edges):
# for input layer, matrix multiply can be converted to be
# an embedding lookup using source node id
embed = weight.view(-1, self.out_feat)
index = edges.data['rel_type'] * self.in_feat + edges.src['id']
return {'msg': embed[index] * edges.data['norm']}
else:
def message_func(edges):
w = weight[edges.data['rel_type']]
msg = torch.bmm(edges.src['h'].unsqueeze(1), w).squeeze()
msg = msg * edges.data['norm']
return {'msg': msg}
def apply_func(nodes):
h = nodes.data['h']
if self.bias:
h = h + self.bias
if self.activation:
h = self.activation(h)
return {'h': h}
g.update_all(message_func, fn.sum(msg='msg', out='h'), apply_func)
###############################################################################
# Full R-GCN model defined
# ~~~~~~~~~~~~~~~~~~~~~~~
class Model(nn.Module):
def __init__(self, num_nodes, h_dim, out_dim, num_rels,
num_bases=-1, num_hidden_layers=1):
super(Model, self).__init__()
self.num_nodes = num_nodes
self.h_dim = h_dim
self.out_dim = out_dim
self.num_rels = num_rels
self.num_bases = num_bases
self.num_hidden_layers = num_hidden_layers
# create rgcn layers
self.build_model()
# create initial features
self.features = self.create_features()
def build_model(self):
self.layers = nn.ModuleList()
# input to hidden
i2h = self.build_input_layer()
self.layers.append(i2h)
# hidden to hidden
for _ in range(self.num_hidden_layers):
h2h = self.build_hidden_layer()
self.layers.append(h2h)
# hidden to output
h2o = self.build_output_layer()
self.layers.append(h2o)
# initialize feature for each node
def create_features(self):
features = torch.arange(self.num_nodes)
return features
def build_input_layer(self):
return RGCNLayer(self.num_nodes, self.h_dim, self.num_rels, self.num_bases,
activation=F.relu, is_input_layer=True)
def build_hidden_layer(self):
return RGCNLayer(self.h_dim, self.h_dim, self.num_rels, self.num_bases,
activation=F.relu)
def build_output_layer(self):
return RGCNLayer(self.h_dim, self.out_dim, self.num_rels, self.num_bases,
activation=partial(F.softmax, dim=1))
def forward(self, g):
if self.features is not None:
g.ndata['id'] = self.features
for layer in self.layers:
layer(g)
return g.ndata.pop('h')
###############################################################################
# Handle dataset
# ~~~~~~~~~~~~~~~~
# This tutorial uses Institute for Applied Informatics and Formal Description Methods (AIFB) dataset from R-GCN paper.
# load graph data
from dgl.contrib.data import load_data
data = load_data(dataset='aifb')
num_nodes = data.num_nodes
num_rels = data.num_rels
num_classes = data.num_classes
labels = data.labels
train_idx = data.train_idx
# split training and validation set
val_idx = train_idx[:len(train_idx) // 5]
train_idx = train_idx[len(train_idx) // 5:]
# edge type and normalization factor
edge_type = torch.from_numpy(data.edge_type)
edge_norm = torch.from_numpy(data.edge_norm).unsqueeze(1)
labels = torch.from_numpy(labels).view(-1)
###############################################################################
# Create graph and model
# ~~~~~~~~~~~~~~~~~~~~~~~
# configurations
n_hidden = 16 # number of hidden units
n_bases = -1 # use number of relations as number of bases
n_hidden_layers = 0 # use 1 input layer, 1 output layer, no hidden layer
n_epochs = 25 # epochs to train
lr = 0.01 # learning rate
l2norm = 0 # L2 norm coefficient
# create graph
g = DGLGraph((data.edge_src, data.edge_dst))
g.edata.update({'rel_type': edge_type, 'norm': edge_norm})
# create model
model = Model(g.num_nodes(),
n_hidden,
num_classes,
num_rels,
num_bases=n_bases,
num_hidden_layers=n_hidden_layers)
###############################################################################
# Training loop
# ~~~~~~~~~~~~~~~~
# optimizer
optimizer = torch.optim.Adam(model.parameters(), lr=lr, weight_decay=l2norm)
print("start training...")
model.train()
for epoch in range(n_epochs):
optimizer.zero_grad()
logits = model.forward(g)
loss = F.cross_entropy(logits[train_idx], labels[train_idx])
loss.backward()
optimizer.step()
train_acc = torch.sum(logits[train_idx].argmax(dim=1) == labels[train_idx])
train_acc = train_acc.item() / len(train_idx)
val_loss = F.cross_entropy(logits[val_idx], labels[val_idx])
val_acc = torch.sum(logits[val_idx].argmax(dim=1) == labels[val_idx])
val_acc = val_acc.item() / len(val_idx)
print("Epoch {:05d} | ".format(epoch) +
"Train Accuracy: {:.4f} | Train Loss: {:.4f} | ".format(
train_acc, loss.item()) +
"Validation Accuracy: {:.4f} | Validation loss: {:.4f}".format(
val_acc, val_loss.item()))
###############################################################################
# .. _link-prediction:
#
# The second task, link prediction
# --------------------------------
# So far, you have seen how to use DGL to implement entity classification with an
# R-GCN model. In the knowledge base setting, representation generated by
# R-GCN can be used to uncover potential relationships between nodes. In the
# R-GCN paper, the authors feed the entity representations generated by R-GCN
# into the `DistMult `_ prediction model
# to predict possible relationships.
#
# The implementation is similar to that presented here, but with an extra DistMult layer
# stacked on top of the R-GCN layers. You can find the complete
# implementation of link prediction with R-GCN in our `Github Python code
# example `_.