From 5eef31db7b84b348bc0f63d10c436d6bef58a95b Mon Sep 17 00:00:00 2001 From: Aurora Rossi Date: Wed, 25 Dec 2024 17:45:41 +0100 Subject: [PATCH] Add node_classification literate src --- .../node_classification.jl | 275 ++ .../node_classification_pluto.jl | 2472 ----------------- 2 files changed, 275 insertions(+), 2472 deletions(-) create mode 100644 GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification.jl delete mode 100644 GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification_pluto.jl diff --git a/GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification.jl b/GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification.jl new file mode 100644 index 000000000..16e82eee8 --- /dev/null +++ b/GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification.jl @@ -0,0 +1,275 @@ +# # Node Classification with Graph Neural Networks + +# In this tutorial, we will be learning how to use Graph Neural Networks (GNNs) for node classification. Given the ground-truth labels of only a small subset of nodes, and want to infer the labels for all the remaining nodes (transductive learning). + +# ## Import +# Let us start off by importing some libraries. We will be using `Flux.jl` and `GraphNeuralNetworks.jl` for our tutorial. + +using Flux, GraphNeuralNetworks +using Flux: onecold, onehotbatch, logitcrossentropy +using MLDatasets +using Plots, TSne +using Statistics, Random + +ENV["DATADEPS_ALWAYS_ACCEPT"] = "true" # don't ask for dataset download confirmation +Random.seed!(17); # for reproducibility + +# ## Visualize +# We want to visualize our results using t-distributed stochastic neighbor embedding (tsne) to project our output onto a 2D plane. + +function visualize_tsne(out, targets) + z = tsne(out, 2) + scatter(z[:, 1], z[:, 2], color = Int.(targets[1:size(z, 1)]), leg = false) +end; + +# ## Dataset: Cora + +# For our tutorial, we will be using the `Cora` dataset. `Cora` is a citation network of 2708 documents categorized into seven classes with 5,429 citation links. Each node represents an article or document, and edges between nodes indicate a citation relationship, where one cites the other. + +# Each publication in the dataset is described by a 0/1-valued word vector indicating the absence/presence of the corresponding word from the dictionary. The dictionary consists of 1433 unique words. + +# This dataset was first introduced by [Yang et al. (2016)](https://arxiv.org/abs/1603.08861) as one of the datasets of the `Planetoid` benchmark suite. We will be using [MLDatasets.jl](https://juliaml.github.io/MLDatasets.jl/stable/) for an easy access to this dataset. + +dataset = Cora() + +# Datasets in MLDatasets.jl have `metadata` containing information about the dataset itself. + +dataset.metadata + +# The `graphs` variable contains the graph. The `Cora` dataset contains only 1 graph. + + +dataset.graphs + +# There is only one graph of the dataset. The `node_data` contains `features` indicating if certain words are present or not and `targets` indicating the class for each document. We convert the single-graph dataset to a `GNNGraph`. + +g = mldataset2gnngraph(dataset) + +println("Number of nodes: $(g.num_nodes)") +println("Number of edges: $(g.num_edges)") +println("Average node degree: $(g.num_edges / g.num_nodes)") +println("Number of training nodes: $(sum(g.ndata.train_mask))") +println("Training node label rate: $(mean(g.ndata.train_mask))") +println("Has isolated nodes: $(has_isolated_nodes(g))") +println("Has self-loops: $(has_self_loops(g))") +println("Is undirected: $(is_bidirected(g))") + + +# Overall, this dataset is quite similar to the previously used [`KarateClub`](https://juliaml.github.io/MLDatasets.jl/stable/datasets/graphs/#MLDatasets.KarateClub) network. +# We can see that the `Cora` network holds 2,708 nodes and 10,556 edges, resulting in an average node degree of 3.9. +# For training this dataset, we are given the ground-truth categories of 140 nodes (20 for each class). +# This results in a training node label rate of only 5%. + +# We can further see that this network is undirected, and that there exists no isolated nodes (each document has at least one citation). + +x = g.ndata.features # we onehot encode both the node labels (what we want to predict): +y = onehotbatch(g.ndata.targets, 1:7) +train_mask = g.ndata.train_mask +num_features = size(x)[1] +hidden_channels = 16 +num_classes = dataset.metadata["num_classes"]; + +# ## Multi-layer Perception Network (MLP) + +# In theory, we should be able to infer the category of a document solely based on its content, *i.e.* its bag-of-words feature representation, without taking any relational information into account. + +# Let's verify that by constructing a simple MLP that solely operates on input node features (using shared weights across all nodes): + +struct MLP + layers::NamedTuple +end + +Flux.@layer :expand MLP + +function MLP(num_features, num_classes, hidden_channels; drop_rate = 0.5) + layers = (hidden = Dense(num_features => hidden_channels), + drop = Dropout(drop_rate), + classifier = Dense(hidden_channels => num_classes)) + return MLP(layers) +end; + +function (model::MLP)(x::AbstractMatrix) + l = model.layers + x = l.hidden(x) + x = relu(x) + x = l.drop(x) + x = l.classifier(x) + return x +end; + +# ### Training a Multilayer Perceptron + +# Our MLP is defined by two linear layers and enhanced by [ReLU](https://fluxml.ai/Flux.jl/stable/models/nnlib/#NNlib.relu) non-linearity and [Dropout](https://fluxml.ai/Flux.jl/stable/models/layers/#Flux.Dropout). +# Here, we first reduce the 1433-dimensional feature vector to a low-dimensional embedding (`hidden_channels=16`), while the second linear layer acts as a classifier that should map each low-dimensional node embedding to one of the 7 classes. + +# Let's train our simple MLP by following a similar procedure as described in [the first part of this tutorial](https://juliagraphs.org/GraphNeuralNetworks.jl/docs/GraphNeuralNetworks.jl/stable/tutorials/gnn_intro/). +# We again make use of the **cross entropy loss** and **Adam optimizer**. +# This time, we also define a **`accuracy` function** to evaluate how well our final model performs on the test node set (which labels have not been observed during training). + +function train(model::MLP, data::AbstractMatrix, epochs::Int, opt) + Flux.trainmode!(model) + + for epoch in 1:epochs + loss, grad = Flux.withgradient(model) do model + ŷ = model(data) + logitcrossentropy(ŷ[:, train_mask], y[:, train_mask]) + end + + Flux.update!(opt, model, grad[1]) + if epoch % 200 == 0 + @show epoch, loss + end + end +end; + +function accuracy(model::MLP, x::AbstractMatrix, y::Flux.OneHotArray, mask::BitVector) + Flux.testmode!(model) + mean(onecold(model(x))[mask] .== onecold(y)[mask]) +end; + +mlp = MLP(num_features, num_classes, hidden_channels) +opt_mlp = Flux.setup(Adam(1e-3), mlp) +epochs = 2000 +train(mlp, g.ndata.features, epochs, opt_mlp) + +# After training the model, we can call the `accuracy` function to see how well our model performs on unseen labels. +# Here, we are interested in the accuracy of the model, *i.e.*, the ratio of correctly classified nodes: + +accuracy(mlp, g.ndata.features, y, .!train_mask) + + +# As one can see, our MLP performs rather bad with only about ~50% test accuracy. +# But why does the MLP do not perform better? +# The main reason for that is that this model suffers from heavy overfitting due to only having access to a **small amount of training nodes**, and therefore generalizes poorly to unseen node representations. + +# It also fails to incorporate an important bias into the model: **Cited papers are very likely related to the category of a document**. +# That is exactly where Graph Neural Networks come into play and can help to boost the performance of our model. + + + +# ## Training a Graph Convolutional Neural Network (GNN) + +# Following-up on the first part of this tutorial, we replace the `Dense` linear layers by the [`GCNConv`](https://juliagraphs.org/GraphNeuralNetworks.jl/docs/GraphNeuralNetworks.jl/stable/api/conv/#GraphNeuralNetworks.GCNConv) module. +# To recap, the **GCN layer** ([Kipf et al. (2017)](https://arxiv.org/abs/1609.02907)) is defined as + +# ```math +# \mathbf{x}_v^{(\ell + 1)} = \mathbf{W}^{(\ell + 1)} \sum_{w \in \mathcal{N}(v) \, \cup \, \{ v \}} \frac{1}{c_{w,v}} \cdot \mathbf{x}_w^{(\ell)} +# ``` + +# where $\mathbf{W}^{(\ell + 1)}$ denotes a trainable weight matrix of shape `[num_output_features, num_input_features]` and $c_{w,v}$ refers to a fixed normalization coefficient for each edge. +# In contrast, a single `Linear` layer is defined as + +# ```math +# \mathbf{x}_v^{(\ell + 1)} = \mathbf{W}^{(\ell + 1)} \mathbf{x}_v^{(\ell)} +# ``` + +# which does not make use of neighboring node information. + +struct GCN + layers::NamedTuple +end + +Flux.@layer GCN # provides parameter collection, gpu movement and more + +function GCN(num_features, num_classes, hidden_channels; drop_rate = 0.5) + layers = (conv1 = GCNConv(num_features => hidden_channels), + drop = Dropout(drop_rate), + conv2 = GCNConv(hidden_channels => num_classes)) + return GCN(layers) +end; + +function (gcn::GCN)(g::GNNGraph, x::AbstractMatrix) + l = gcn.layers + x = l.conv1(g, x) + x = relu.(x) + x = l.drop(x) + x = l.conv2(g, x) + return x +end; + + +# Now let's visualize the node embeddings of our **untrained** GCN network. + +gcn = GCN(num_features, num_classes, hidden_channels) +h_untrained = gcn(g, x) |> transpose +visualize_tsne(h_untrained, g.ndata.targets) + + +# We certainly can do better by training our model. +# The training and testing procedure is once again the same, but this time we make use of the node features `x` **and** the graph `g` as input to our GCN model. + +function train(model::GCN, g::GNNGraph, x::AbstractMatrix, epochs::Int, opt) + Flux.trainmode!(model) + + for epoch in 1:epochs + loss, grad = Flux.withgradient(model) do model + ŷ = model(g, x) + logitcrossentropy(ŷ[:, train_mask], y[:, train_mask]) + end + + Flux.update!(opt, model, grad[1]) + if epoch % 200 == 0 + @show epoch, loss + end + end +end; + +# + +mlp = MLP(num_features, num_classes, hidden_channels) +opt_mlp = Flux.setup(Adam(1e-3), mlp) +epochs = 2000 +train(mlp, g.ndata.features, epochs, opt_mlp) + +# +function accuracy(model::GCN, g::GNNGraph, x::AbstractMatrix, y::Flux.OneHotArray, + mask::BitVector) + Flux.testmode!(model) + mean(onecold(model(g, x))[mask] .== onecold(y)[mask]) +end + +# + +accuracy(mlp, g.ndata.features, y, .!train_mask) + +# + +opt_gcn = Flux.setup(Adam(1e-2), gcn) +train(gcn, g, x, epochs, opt_gcn) + + +# Now let's evaluate the loss of our trained GCN. + +train_accuracy = accuracy(gcn, g, g.ndata.features, y, train_mask) +test_accuracy = accuracy(gcn, g, g.ndata.features, y, .!train_mask) + +println("Train accuracy: $(train_accuracy)") +println("Test accuracy: $(test_accuracy)") + + +# **There it is!** +# By simply swapping the linear layers with GNN layers, we can reach **76% of test accuracy**! +# This is in stark contrast to the 59% of test accuracy obtained by our MLP, indicating that relational information plays a crucial role in obtaining better performance. + +# We can also verify that once again by looking at the output embeddings of our trained model, which now produces a far better clustering of nodes of the same category. + + +Flux.testmode!(gcn) # inference mode + +out_trained = gcn(g, x) |> transpose +visualize_tsne(out_trained, g.ndata.targets) + + + +# ## (Optional) Exercises + +# 1. To achieve better model performance and to avoid overfitting, it is usually a good idea to select the best model based on an additional validation set. The `Cora` dataset provides a validation node set as `g.ndata.val_mask`, but we haven't used it yet. Can you modify the code to select and test the model with the highest validation performance? This should bring test performance to **82% accuracy**. + +# 2. How does `GCN` behave when increasing the hidden feature dimensionality or the number of layers? Does increasing the number of layers help at all? + +# 3. You can try to use different GNN layers to see how model performance changes. What happens if you swap out all `GCNConv` instances with [`GATConv`](https://juliagraphs.org/GraphNeuralNetworks.jl/docs/GraphNeuralNetworks.jl/stable/api/conv/#GraphNeuralNetworks.GATConv) layers that make use of attention? Try to write a 2-layer `GAT` model that makes use of 8 attention heads in the first layer and 1 attention head in the second layer, uses a `dropout` ratio of `0.6` inside and outside each `GATConv` call, and uses a `hidden_channels` dimensions of `8` per head. + + + +# ## Conclusion +# In this tutorial, we have seen how to apply GNNs to real-world problems, and, in particular, how they can effectively be used for boosting a model's performance. In the next tutorial, we will look into how GNNs can be used for the task of graph classification. diff --git a/GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification_pluto.jl b/GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification_pluto.jl deleted file mode 100644 index 7e622b0ba..000000000 --- a/GraphNeuralNetworks/docs/src_tutorials/introductory_tutorials/node_classification_pluto.jl +++ /dev/null @@ -1,2472 +0,0 @@ -### A Pluto.jl notebook ### -# v0.19.45 - -#> [frontmatter] -#> author = "[Deeptendu Santra](https://github.com/Dsantra92)" -#> title = "Node Classification with Graph Neural Networks" -#> date = "2022-09-25" -#> description = "Tutorial for Node classification using GraphNeuralNetworks.jl" -#> cover = "assets/node_classsification.gif" - -using Markdown -using InteractiveUtils - -# ╔═╡ 5463330a-0161-11ed-1b18-936030a32bbf -# ╠═╡ show_logs = false -begin - using MLDatasets - using GraphNeuralNetworks - using Flux - using Flux: onecold, onehotbatch, logitcrossentropy - using Plots - using PlutoUI - using TSne - using Random - using Statistics - - ENV["DATADEPS_ALWAYS_ACCEPT"] = "true" - Random.seed!(17) # for reproducibility -end; - -# ╔═╡ ca2f0293-7eac-4d9a-9a2f-fda47fd95a99 -md""" -# Node Classification with Graph Neural Networks - -In this tutorial, we will be learning how to use Graph Neural Networks (GNNs) for node classification. Given the ground-truth labels of only a small subset of nodes, and want to infer the labels for all the remaining nodes (transductive learning). -""" - -# ╔═╡ 4455f18c-2bd9-42ed-bce3-cfe6561eab23 -md""" -## Import -Let us start off by importing some libraries. We will be using Flux.jl and `GraphNeuralNetworks.jl` for our tutorial. -""" - -# ╔═╡ 0d556a7c-d4b6-4cef-806c-3e1712de0791 -md""" -## Visualize -We want to visualize the outputs of the results using t-distributed stochastic neighbor embedding (tsne) to embed our output embeddings onto a 2D plane. -""" - -# ╔═╡ 997b5387-3811-4998-a9d1-7981b58b9e09 -function visualize_tsne(out, targets) - z = tsne(out, 2) - scatter(z[:, 1], z[:, 2], color = Int.(targets[1:size(z, 1)]), leg = false) -end - -# ╔═╡ 4b6fa18d-7ccd-4c07-8dc3-ded4d7da8562 -md""" -## Dataset: Cora - -For our tutorial, we will be using the `Cora` dataset. `Cora` is a citation network of 2708 documents classified into one of seven classes and 5429 links. Each node represent articles/documents and the edges between these nodes if one of them cite each other. - -Each publication in the dataset is described by a 0/1-valued word vector indicating the absence/presence of the corresponding word from the dictionary. The dictionary consists of 1433 unique words. - -This dataset was first introduced by [Yang et al. (2016)](https://arxiv.org/abs/1603.08861) as one of the datasets of the `Planetoid` benchmark suite. We will be using [MLDatasets.jl](https://juliaml.github.io/MLDatasets.jl/stable/) for an easy access to this dataset. -""" - -# ╔═╡ edab1e3a-31f6-471f-9835-5b1f97e5cf3f -dataset = Cora() - -# ╔═╡ d73a2db5-9417-4b2c-a9f5-b7d499a53fcb -md""" -Datasets in MLDatasets.jl have `metadata` containing information about the dataset itself. -""" - -# ╔═╡ 32bb90c1-c802-4c0c-a620-5d3b8f3f2477 -dataset.metadata - -# ╔═╡ 3438ee7f-bfca-465d-85df-13379622d415 -md""" -The `graphs` variable GraphDataset contains the graph. The `Cora` dataset contains only 1 graph. -""" - -# ╔═╡ eec6fb60-0774-4f2a-bcb7-dbc28ab747a6 -dataset.graphs - -# ╔═╡ bd2fd04d-7fb0-4b31-959b-bddabe681754 -md""" -There is only one graph of the dataset. The `node_data` contains `features` indicating if certain words are present or not and `targets` indicating the class for each document. We convert the single-graph dataset to a `GNNGraph`. -""" - -# ╔═╡ b29c3a02-c21b-4b10-aa04-b90bcc2931d8 -g = mldataset2gnngraph(dataset) - -# ╔═╡ 16d9fbad-d4dc-4b51-9576-1736d228e2b3 -with_terminal() do - # Gather some statistics about the graph. - println("Number of nodes: $(g.num_nodes)") - println("Number of edges: $(g.num_edges)") - println("Average node degree: $(g.num_edges / g.num_nodes)") - println("Number of training nodes: $(sum(g.ndata.train_mask))") - println("Training node label rate: $(mean(g.ndata.train_mask))") - # println("Has isolated nodes: $(has_isolated_nodes(g))") - println("Has self-loops: $(has_self_loops(g))") - println("Is undirected: $(is_bidirected(g))") -end - -# ╔═╡ 923d061c-25c3-4826-8147-9afa3dbd5bac -md""" -Overall, this dataset is quite similar to the previously used [`KarateClub`](https://juliaml.github.io/MLDatasets.jl/stable/datasets/graphs/#MLDatasets.KarateClub) network. -We can see that the `Cora` network holds 2,708 nodes and 10,556 edges, resulting in an average node degree of 3.9. -For training this dataset, we are given the ground-truth categories of 140 nodes (20 for each class). -This results in a training node label rate of only 5%. - -We can further see that this network is undirected, and that there exists no isolated nodes (each document has at least one citation). -""" - -# ╔═╡ 28e00b95-56db-4d36-a205-fd24d3c54e17 -begin - x = g.ndata.features - # we onehot encode both the node labels (what we want to predict): - y = onehotbatch(g.ndata.targets, 1:7) - train_mask = g.ndata.train_mask - num_features = size(x)[1] - hidden_channels = 16 - num_classes = dataset.metadata["num_classes"] -end; - -# ╔═╡ fa743000-604f-4d28-99f1-46ab2f884b8e -md""" -## Multi-layer Perception Network (MLP) - -In theory, we should be able to infer the category of a document solely based on its content, *i.e.* its bag-of-words feature representation, without taking any relational information into account. - -Let's verify that by constructing a simple MLP that solely operates on input node features (using shared weights across all nodes): -""" - -# ╔═╡ f972f61b-2001-409b-9190-ac2c0652829a -begin - struct MLP - layers::NamedTuple - end - - Flux.@layer :expand MLP - - function MLP(num_features, num_classes, hidden_channels; drop_rate = 0.5) - layers = (hidden = Dense(num_features => hidden_channels), - drop = Dropout(drop_rate), - classifier = Dense(hidden_channels => num_classes)) - return MLP(layers) - end - - function (model::MLP)(x::AbstractMatrix) - l = model.layers - x = l.hidden(x) - x = relu(x) - x = l.drop(x) - x = l.classifier(x) - return x - end -end - -# ╔═╡ 4dade64a-e28e-42c7-8ad5-93fc04724d4d -md""" -### Training a Multilayer Perceptron - -Our MLP is defined by two linear layers and enhanced by [ReLU](https://fluxml.ai/Flux.jl/stable/models/nnlib/#NNlib.relu) non-linearity and [Dropout](https://fluxml.ai/Flux.jl/stable/models/layers/#Flux.Dropout). -Here, we first reduce the 1433-dimensional feature vector to a low-dimensional embedding (`hidden_channels=16`), while the second linear layer acts as a classifier that should map each low-dimensional node embedding to one of the 7 classes. - -Let's train our simple MLP by following a similar procedure as described in [the first part of this tutorial](https://carlolucibello.github.io/GraphNeuralNetworks.jl/dev/tutorials/introductory_tutorials/gnn_intro_pluto/#Hands-on-introduction-to-Graph-Neural-Networks). -We again make use of the **cross entropy loss** and **Adam optimizer**. -This time, we also define a **`accuracy` function** to evaluate how well our final model performs on the test node set (which labels have not been observed during training). -""" - -# ╔═╡ 05979cfe-439c-4abc-90cd-6ca2a05f6e0f -function train(model::MLP, data::AbstractMatrix, epochs::Int, opt) - Flux.trainmode!(model) - - for epoch in 1:epochs - loss, grad = Flux.withgradient(model) do model - ŷ = model(data) - logitcrossentropy(ŷ[:, train_mask], y[:, train_mask]) - end - - Flux.update!(opt, model, grad[1]) - if epoch % 200 == 0 - @show epoch, loss - end - end -end - -# ╔═╡ a3f420e1-7521-4df9-b6d5-fc0a1fd05095 -function accuracy(model::MLP, x::AbstractMatrix, y::Flux.OneHotArray, mask::BitVector) - Flux.testmode!(model) - mean(onecold(model(x))[mask] .== onecold(y)[mask]) -end - -# ╔═╡ b18384fe-b8ae-4f51-bd73-d129d5e70f98 -md""" -After training the model, we can call the `accuracy` function to see how well our model performs on unseen labels. -Here, we are interested in the accuracy of the model, *i.e.*, the ratio of correctly classified nodes: -""" - -# ╔═╡ 54a2972e-b107-47c8-bf7e-eb51b4ccbe02 -md""" -As one can see, our MLP performs rather bad with only about 47% test accuracy. -But why does the MLP do not perform better? -The main reason for that is that this model suffers from heavy overfitting due to only having access to a **small amount of training nodes**, and therefore generalizes poorly to unseen node representations. - -It also fails to incorporate an important bias into the model: **Cited papers are very likely related to the category of a document**. -That is exactly where Graph Neural Networks come into play and can help to boost the performance of our model. -""" - -# ╔═╡ 623e7b53-046c-4858-89d9-13caae45255d -md""" -## Training a Graph Convolutional Neural Network (GNN) - -Following-up on [the first part of this tutorial](https://carlolucibello.github.io/GraphNeuralNetworks.jl/dev/tutorials/introductory_tutorials/node_classification_pluto/#Multi-layer-Perception-Network-(MLP)), we replace the `Dense` linear layers by the [`GCNConv`](https://carlolucibello.github.io/GraphNeuralNetworks.jl/dev/api/conv/#GraphNeuralNetworks.GCNConv) module. -To recap, the **GCN layer** ([Kipf et al. (2017)](https://arxiv.org/abs/1609.02907)) is defined as - -```math -\mathbf{x}_v^{(\ell + 1)} = \mathbf{W}^{(\ell + 1)} \sum_{w \in \mathcal{N}(v) \, \cup \, \{ v \}} \frac{1}{c_{w,v}} \cdot \mathbf{x}_w^{(\ell)} -``` - -where ``\mathbf{W}^{(\ell + 1)}`` denotes a trainable weight matrix of shape `[num_output_features, num_input_features]` and $c_{w,v}$ refers to a fixed normalization coefficient for each edge. -In contrast, a single `Linear` layer is defined as - -```math -\mathbf{x}_v^{(\ell + 1)} = \mathbf{W}^{(\ell + 1)} \mathbf{x}_v^{(\ell)} -``` - -which does not make use of neighboring node information. -""" - -# ╔═╡ eb36a46c-f139-425e-8a93-207bc4a16f89 -begin - struct GCN - layers::NamedTuple - end - - Flux.@layer GCN # provides parameter collection, gpu movement and more - - function GCN(num_features, num_classes, hidden_channels; drop_rate = 0.5) - layers = (conv1 = GCNConv(num_features => hidden_channels), - drop = Dropout(drop_rate), - conv2 = GCNConv(hidden_channels => num_classes)) - return GCN(layers) - end - - function (gcn::GCN)(g::GNNGraph, x::AbstractMatrix) - l = gcn.layers - x = l.conv1(g, x) - x = relu.(x) - x = l.drop(x) - x = l.conv2(g, x) - return x - end -end - -# ╔═╡ 20b5f802-abce-49e1-a442-f381e80c0f85 -md""" -Now let's visualize the node embeddings of our **untrained** GCN network. -""" - -# ╔═╡ b295adce-b37e-45f3-963a-3699d714e36d -# ╠═╡ show_logs = false -begin - gcn = GCN(num_features, num_classes, hidden_channels) - h_untrained = gcn(g, x) |> transpose - visualize_tsne(h_untrained, g.ndata.targets) -end - -# ╔═╡ 5538970f-b273-4122-9d50-7deb049e6934 -md""" -We certainly can do better by training our model. -The training and testing procedure is once again the same, but this time we make use of the node features `x` **and** the graph `g` as input to our GCN model. -""" - -# ╔═╡ 901d9478-9a12-4122-905d-6cfc6d80e84c -function train(model::GCN, g::GNNGraph, x::AbstractMatrix, epochs::Int, opt) - Flux.trainmode!(model) - - for epoch in 1:epochs - loss, grad = Flux.withgradient(model) do model - ŷ = model(g, x) - logitcrossentropy(ŷ[:, train_mask], y[:, train_mask]) - end - - Flux.update!(opt, model, grad[1]) - if epoch % 200 == 0 - @show epoch, loss - end - end -end - -# ╔═╡ 026911dd-6a27-49ce-9d41-21e01646c10a -# ╠═╡ show_logs = false -begin - mlp = MLP(num_features, num_classes, hidden_channels) - opt_mlp = Flux.setup(Adam(1e-3), mlp) - epochs = 2000 - train(mlp, g.ndata.features, epochs, opt_mlp) -end - -# ╔═╡ 65d9fd3d-1649-4b95-a106-f26fa4ab9bce -function accuracy(model::GCN, g::GNNGraph, x::AbstractMatrix, y::Flux.OneHotArray, - mask::BitVector) - Flux.testmode!(model) - mean(onecold(model(g, x))[mask] .== onecold(y)[mask]) -end - -# ╔═╡ b2302697-1e20-4721-ae93-0b121ff9ce8f -accuracy(mlp, g.ndata.features, y, .!train_mask) - -# ╔═╡ 20be52b1-1c33-4f54-b5c0-fecc4e24fbb5 -# ╠═╡ show_logs = false -begin - opt_gcn = Flux.setup(Adam(1e-2), gcn) - train(gcn, g, x, epochs, opt_gcn) -end - -# ╔═╡ 5aa99aff-b5ed-40ec-a7ec-0ba53385e6bd -md""" -Now let's evaluate the loss of our trained GCN. -""" - -# ╔═╡ 2163d0d8-0661-4d11-a09e-708769011d35 -with_terminal() do - train_accuracy = accuracy(gcn, g, g.ndata.features, y, train_mask) - test_accuracy = accuracy(gcn, g, g.ndata.features, y, .!train_mask) - - println("Train accuracy: $(train_accuracy)") - println("Test accuracy: $(test_accuracy)") -end - -# ╔═╡ 6cd49f3f-a415-4b6a-9323-4d6aa6b87f18 -md""" -**There it is!** -By simply swapping the linear layers with GNN layers, we can reach **75.77% of test accuracy**! -This is in stark contrast to the 59% of test accuracy obtained by our MLP, indicating that relational information plays a crucial role in obtaining better performance. - -We can also verify that once again by looking at the output embeddings of our trained model, which now produces a far better clustering of nodes of the same category. -""" - -# ╔═╡ 7a93a802-6774-42f9-b6da-7ae614464e72 -# ╠═╡ show_logs = false -begin - Flux.testmode!(gcn) # inference mode - - out_trained = gcn(g, x) |> transpose - visualize_tsne(out_trained, g.ndata.targets) -end - -# ╔═╡ 50a409fd-d80b-4c48-a51b-173c39a6dcb4 -md""" -## (Optional) Exercises - -1. To achieve better model performance and to avoid overfitting, it is usually a good idea to select the best model based on an additional validation set. The `Cora` dataset provides a validation node set as `g.ndata.val_mask`, but we haven't used it yet. Can you modify the code to select and test the model with the highest validation performance? This should bring test performance to **82% accuracy**. - -2. How does `GCN` behave when increasing the hidden feature dimensionality or the number of layers? Does increasing the number of layers help at all? - -3. You can try to use different GNN layers to see how model performance changes. What happens if you swap out all `GCNConv` instances with [`GATConv`](https://carlolucibello.github.io/GraphNeuralNetworks.jl/dev/api/conv/#GraphNeuralNetworks.GATConv) layers that make use of attention? Try to write a 2-layer `GAT` model that makes use of 8 attention heads in the first layer and 1 attention head in the second layer, uses a `dropout` ratio of `0.6` inside and outside each `GATConv` call, and uses a `hidden_channels` dimensions of `8` per head. -""" - -# ╔═╡ c343419f-a1d7-45a0-b600-2c868588b33a -md""" -## Conclusion -In this tutorial, we have seen how to apply GNNs to real-world problems, and, in particular, how they can effectively be used for boosting a model's performance. In the next tutorial, we will look into how GNNs can be used for the task of graph classification. -""" - -# ╔═╡ 00000000-0000-0000-0000-000000000001 -PLUTO_PROJECT_TOML_CONTENTS = """ -[deps] -Flux = "587475ba-b771-5e3f-ad9e-33799f191a9c" -GraphNeuralNetworks = "cffab07f-9bc2-4db1-8861-388f63bf7694" -MLDatasets = "eb30cadb-4394-5ae3-aed4-317e484a6458" -Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80" -PlutoUI = "7f904dfe-b85e-4ff6-b463-dae2292396a8" -Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c" -Statistics = "10745b16-79ce-11e8-11f9-7d13ad32a3b2" -TSne = "24678dba-d5e9-5843-a4c6-250288b04835" - -[compat] -Flux = "~0.14.16" -GraphNeuralNetworks = "~0.6.19" -MLDatasets = "~0.7.16" -Plots = "~1.40.5" -PlutoUI = "~0.7.59" -TSne = "~1.3.0" -""" - -# ╔═╡ 00000000-0000-0000-0000-000000000002 -PLUTO_MANIFEST_TOML_CONTENTS = """ -# This file is machine-generated - editing it directly is not advised - -julia_version = "1.10.4" -manifest_format = "2.0" -project_hash = "fb2b669c9e43473fabf01e07c834a510ae36fa5e" - 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-[[deps.xkbcommon_jll]] -deps = ["Artifacts", "JLLWrappers", "Libdl", "Pkg", "Wayland_jll", "Wayland_protocols_jll", "Xorg_libxcb_jll", "Xorg_xkeyboard_config_jll"] -git-tree-sha1 = "9c304562909ab2bab0262639bd4f444d7bc2be37" -uuid = "d8fb68d0-12a3-5cfd-a85a-d49703b185fd" -version = "1.4.1+1" -""" - -# ╔═╡ Cell order: -# ╟─ca2f0293-7eac-4d9a-9a2f-fda47fd95a99 -# ╟─4455f18c-2bd9-42ed-bce3-cfe6561eab23 -# ╠═5463330a-0161-11ed-1b18-936030a32bbf -# ╟─0d556a7c-d4b6-4cef-806c-3e1712de0791 -# ╠═997b5387-3811-4998-a9d1-7981b58b9e09 -# ╟─4b6fa18d-7ccd-4c07-8dc3-ded4d7da8562 -# ╠═edab1e3a-31f6-471f-9835-5b1f97e5cf3f -# ╟─d73a2db5-9417-4b2c-a9f5-b7d499a53fcb -# ╠═32bb90c1-c802-4c0c-a620-5d3b8f3f2477 -# ╟─3438ee7f-bfca-465d-85df-13379622d415 -# ╠═eec6fb60-0774-4f2a-bcb7-dbc28ab747a6 -# ╟─bd2fd04d-7fb0-4b31-959b-bddabe681754 -# ╠═b29c3a02-c21b-4b10-aa04-b90bcc2931d8 -# ╠═16d9fbad-d4dc-4b51-9576-1736d228e2b3 -# ╟─923d061c-25c3-4826-8147-9afa3dbd5bac -# ╠═28e00b95-56db-4d36-a205-fd24d3c54e17 -# ╟─fa743000-604f-4d28-99f1-46ab2f884b8e -# ╠═f972f61b-2001-409b-9190-ac2c0652829a -# ╟─4dade64a-e28e-42c7-8ad5-93fc04724d4d -# ╠═05979cfe-439c-4abc-90cd-6ca2a05f6e0f -# ╠═a3f420e1-7521-4df9-b6d5-fc0a1fd05095 -# ╠═026911dd-6a27-49ce-9d41-21e01646c10a -# ╟─b18384fe-b8ae-4f51-bd73-d129d5e70f98 -# ╠═b2302697-1e20-4721-ae93-0b121ff9ce8f -# ╟─54a2972e-b107-47c8-bf7e-eb51b4ccbe02 -# ╟─623e7b53-046c-4858-89d9-13caae45255d -# ╠═eb36a46c-f139-425e-8a93-207bc4a16f89 -# ╟─20b5f802-abce-49e1-a442-f381e80c0f85 -# ╠═b295adce-b37e-45f3-963a-3699d714e36d -# ╟─5538970f-b273-4122-9d50-7deb049e6934 -# ╠═901d9478-9a12-4122-905d-6cfc6d80e84c -# ╠═65d9fd3d-1649-4b95-a106-f26fa4ab9bce -# ╠═20be52b1-1c33-4f54-b5c0-fecc4e24fbb5 -# ╟─5aa99aff-b5ed-40ec-a7ec-0ba53385e6bd -# ╠═2163d0d8-0661-4d11-a09e-708769011d35 -# ╟─6cd49f3f-a415-4b6a-9323-4d6aa6b87f18 -# ╠═7a93a802-6774-42f9-b6da-7ae614464e72 -# ╟─50a409fd-d80b-4c48-a51b-173c39a6dcb4 -# ╟─c343419f-a1d7-45a0-b600-2c868588b33a -# ╟─00000000-0000-0000-0000-000000000001 -# ╟─00000000-0000-0000-0000-000000000002