Temporal Graph classification with GraphNeuralNetworks.jl
In this tutorial, we will learn how to extend the graph classification task to the case of temporal graphs, i.e., graphs whose topology and features are time-varying.
We will design and train a simple temporal graph neural network architecture to classify subjects' gender (female or male) using the temporal graphs extracted from their brain fMRI scan signals. Given the large amount of data, we will implement the training so that it can also run on the GPU.
Import
We start by importing the necessary libraries. We use GraphNeuralNetworks.jl
, Flux.jl
and MLDatasets.jl
, among others.
begin
using Flux
using GraphNeuralNetworks
using Statistics, Random
using LinearAlgebra
using MLDatasets: TemporalBrains
using CUDA
using cuDNN
end
Dataset: TemporalBrains
The TemporalBrains dataset contains a collection of functional brain connectivity networks from 1000 subjects obtained from resting-state functional MRI data from the Human Connectome Project (HCP). Functional connectivity is defined as the temporal dependence of neuronal activation patterns of anatomically separated brain regions.
The graph nodes represent brain regions and their number is fixed at 102 for each of the 27 snapshots, while the edges, representing functional connectivity, change over time. For each snapshot, the feature of a node represents the average activation of the node during that snapshot. Each temporal graph has a label representing gender ('M' for male and 'F' for female) and age group (22-25, 26-30, 31-35, and 36+). The network's edge weights are binarized, and the threshold is set to 0.6 by default.
brain_dataset = TemporalBrains()
dataset TemporalBrains: graphs => 1000-element Vector{MLDatasets.TemporalSnapshotsGraph}
After loading the dataset from the MLDatasets.jl package, we see that there are 1000 graphs and we need to convert them to the TemporalSnapshotsGNNGraph
format. So we create a function called data_loader
that implements the latter and splits the dataset into the training set that will be used to train the model and the test set that will be used to test the performance of the model.
function data_loader(brain_dataset)
graphs = brain_dataset.graphs
dataset = Vector{TemporalSnapshotsGNNGraph}(undef, length(graphs))
for i in 1:length(graphs)
graph = graphs[i]
dataset[i] = TemporalSnapshotsGNNGraph(GraphNeuralNetworks.mlgraph2gnngraph.(graph.snapshots))
# Add graph and node features
for t in 1:27
s = dataset[i].snapshots[t]
s.ndata.x = [I(102); s.ndata.x']
end
dataset[i].tgdata.g = Float32.(Flux.onehot(graph.graph_data.g, ["F", "M"]))
end
# Split the dataset into a 80% training set and a 20% test set
train_loader = dataset[1:200]
test_loader = dataset[201:250]
return train_loader, test_loader
end;
The first part of the data_loader
function calls the mlgraph2gnngraph
function for each snapshot, which takes the graph and converts it to a GNNGraph
. The vector of GNNGraph
s is then rewritten to a TemporalSnapshotsGNNGraph
.
The second part adds the graph and node features to the temporal graphs, in particular it adds the one-hot encoding of the label of the graph (in this case we directly use the identity matrix) and appends the mean activation of the node of the snapshot (which is contained in the vector dataset[i].snapshots[t].ndata.x
, where i
is the index indicating the subject and t
is the snapshot). For the graph feature, it adds the one-hot encoding of gender.
The last part splits the dataset.
Model
We now implement a simple model that takes a TemporalSnapshotsGNNGraph
as input. It consists of a GINConv
applied independently to each snapshot, a GlobalPool
to get an embedding for each snapshot, a pooling on the time dimension to get an embedding for the whole temporal graph, and finally a Dense
layer.
First, we start by adapting the GlobalPool
to the TemporalSnapshotsGNNGraphs
.
function (l::GlobalPool)(g::TemporalSnapshotsGNNGraph, x::AbstractVector)
h = [reduce_nodes(l.aggr, g[i], x[i]) for i in 1:(g.num_snapshots)]
sze = size(h[1])
reshape(reduce(hcat, h), sze[1], length(h))
end
Then we implement the constructor of the model, which we call GenderPredictionModel
, and the foward pass.
begin
struct GenderPredictionModel
gin::GINConv
mlp::Chain
globalpool::GlobalPool
f::Function
dense::Dense
end
Flux.@layer GenderPredictionModel
function GenderPredictionModel(; nfeatures = 103, nhidden = 128, activation = relu)
mlp = Chain(Dense(nfeatures, nhidden, activation), Dense(nhidden, nhidden, activation))
gin = GINConv(mlp, 0.5)
globalpool = GlobalPool(mean)
f = x -> mean(x, dims = 2)
dense = Dense(nhidden, 2)
GenderPredictionModel(gin, mlp, globalpool, f, dense)
end
function (m::GenderPredictionModel)(g::TemporalSnapshotsGNNGraph)
h = m.gin(g, g.ndata.x)
h = m.globalpool(g, h)
h = m.f(h)
m.dense(h)
end
end
Training
We train the model for 100 epochs, using the Adam optimizer with a learning rate of 0.001. We use the logitbinarycrossentropy
as the loss function, which is typically used as the loss in two-class classification, where the labels are given in a one-hot format. The accuracy expresses the number of correct classifications.
lossfunction(ŷ, y) = Flux.logitbinarycrossentropy(ŷ, y);
function eval_loss_accuracy(model, data_loader)
error = mean([lossfunction(model(g), g.tgdata.g) for g in data_loader])
acc = mean([round(100 * mean(Flux.onecold(model(g)) .== Flux.onecold(g.tgdata.g)); digits = 2) for g in data_loader])
return (loss = error, acc = acc)
end;
function train(dataset; usecuda::Bool, kws...)
if usecuda && CUDA.functional() #check if GPU is available
my_device = gpu
@info "Training on GPU"
else
my_device = cpu
@info "Training on CPU"
end
function report(epoch)
train_loss, train_acc = eval_loss_accuracy(model, train_loader)
test_loss, test_acc = eval_loss_accuracy(model, test_loader)
println("Epoch: $epoch $((; train_loss, train_acc)) $((; test_loss, test_acc))")
return (train_loss, train_acc, test_loss, test_acc)
end
model = GenderPredictionModel() |> my_device
opt = Flux.setup(Adam(1.0f-3), model)
train_loader, test_loader = data_loader(dataset)
train_loader = train_loader |> my_device
test_loader = test_loader |> my_device
report(0)
for epoch in 1:100
for g in train_loader
grads = Flux.gradient(model) do model
ŷ = model(g)
lossfunction(vec(ŷ), g.tgdata.g)
end
Flux.update!(opt, model, grads[1])
end
if epoch % 10 == 0
report(epoch)
end
end
return model
end;
train(brain_dataset; usecuda = true)
GenderPredictionModel(GINConv(Chain(Dense(103 => 128, relu), Dense(128 => 128, relu)), 0.5), Chain(Dense(103 => 128, relu), Dense(128 => 128, relu)), GlobalPool{typeof(mean)}(Statistics.mean), var"#4#5"(), Dense(128 => 2)) # 30_082 parameters, plus 29_824 non-trainable
We set up the training on the GPU because training takes a lot of time, especially when working on the CPU.
Conclusions
In this tutorial, we implemented a very simple architecture to classify temporal graphs in the context of gender classification using brain data. We then trained the model on the GPU for 100 epochs on the TemporalBrains dataset. The accuracy of the model is approximately 75-80%, but can be improved by fine-tuning the parameters and training on more data.