In the CNN post we described how convolutional neural networks examine an image as if sweeping it with a torch. Each time, the torch lights up a small square: a pixel and its neighbours to the left, right, above and below. That works because in an image every pixel’s neighbours are clearly defined, and everyone has the same number of them.
Now think of an EEG cap. The electrodes don’t sit on a neat grid on the head. Some have four electrodes nearby, some only two. And two electrodes sitting side by side on the head doesn’t mean the brain activity under them is linked. Two distant regions may be working closely together. The structure that best describes this kind of data isn’t a grid but a graph: electrodes as nodes, the relationships between them as edges.
Taking Advice From The Neighbours
Graph convolutional networks (GCNs) put the torch away and use a more social method. Picture an apartment building. Every flat has its own opinion. At a meeting, everyone listens only to their next-door neighbours and updates their own opinion by blending it with theirs. Who counts as whose neighbour is set by the building’s floor plan, the graph.
One GCN layer does exactly this:
- Each node gathers the features of its neighbours.
- It combines them with its own feature.
- It transforms the result with learned weights to produce a new feature.
This simple rule, proposed by Kipf and Welling in 2017, became the field’s most widely used building block.
After one layer, every flat knows what its next-door neighbours think. After the second layer, it knows what its neighbours’ neighbours think too. As layers are added, information ripples outward across the network, just as the area the torch “sees” grows deeper into a CNN.
Who Draws The Floor Plan?
A GCN’s success depends heavily on the graph. For EEG there are a few options:
- Physical distance: Connect electrodes that are close together on the head. The simplest approach.
- Functional connectivity: Connect electrodes whose signals resemble each other, measured with things like correlation or coherence.
- A learned graph: Let the network draw the floor plan itself. DGCNN, proposed by Song and colleagues for EEG emotion recognition, learns the connections between electrodes from the data during training.
The third approach has a nice side effect: once training is done, we can look at the learned floor plan and see which relationships between regions the model relied on to make its decisions.
Why Does It Matter?
In classical methods we extract features from each electrode and line them all up in one long list. Along the way, the relationships between electrodes are lost. A GCN builds those relationships right into the model. Since the brain already works as a network, modelling it as a network is a natural choice.
In our lab we have also worked on combining connectivity between brain regions with deep learning. For example, for ADHD detection we fused connectivity information with deep learning models at the decision level.
References
- Kipf, T. N., Welling, M. (2017). Semi-supervised classification with graph convolutional networks. International Conference on Learning Representations (ICLR). doi:10.48550/arXiv.1609.02907
- Song, T., Zheng, W., Song, P., Cui, Z. (2020). EEG emotion recognition using dynamical graph convolutional neural networks. IEEE Transactions on Affective Computing, 11(3), 532–541. doi:10.1109/TAFFC.2018.2817622
- Karabiber Cura, O., Ciklacandir, F. G., Akan, A., Kocaaslan Atli, S. (2023). Detection of attention deficit hyperactivity disorder using decision-level fusion of brain connectivity information based on deep learning. Medical Technologies Congress (TIPTEKNO). doi:10.1109/tiptekno59875.2023.10359178