The first paper on which I worked during my PhD is about detecting changes in sequences of graphs using non-Euclidean geometry and adversarial autoencoders. As a real-world application of the method presented in the paper, we showed that we could detect epileptic seizures in the brain, by monitoring a stream of functional connectivity brain networks.

In general, the methodology presented in the paper can work for any data that:

1. can be represented as graphs;
2. has a temporal dimension;
3. has a change that you want to identify somewhere along the stream of data;
4. has i.i.d. samples.

There are a lot of temporal networks that can be found in the wild, but not many datasets respect all the requirements at the same time. What’s more, many public datasets have very little samples along the temporal axis.

La Torre d’En Rovira.

We walk under the scorching sun for two hours, in and out of the pine groves where old hippies live in old trucks, not knowing where we’re going except for the fact that we’re moving North. We’re looking for a place to escape the crowded August of the island.

When considering relational problems, the temporal dimension is often crucial to understand whether the process behind the relational graph is evolving, and how; think how often people follow and unfollow each other on Instagram, how the type of content in one’s posts may change over time, and how all of these aspects are echoed throughout the network, interacting with one another in complex ways.

While most works that apply deep learning to temporal networks are focused on the evolution of the graph at the node or edge level, it is extremely interesting to study a graph-based process from a global perspective, at the graph level, to detect trends and changes in the process itself.