I think I’ll spend this week explaining exactly what the 1-dimensional PH features project is about. Now that I have a much better grasp on how the 0-dimensional project works (it only took me nearly an entire year..) I feel I know a bit more about the 1-d project!
When I first approached Dr. Rosen about working together in his lab, the idea was to get started on the 1-dimensional project first. We quickly learned there was still a lot to do and flesh out for the 0-dimensional project. As far as we knew, there was no technique/software to detect the 1-dimensional PH features of a graph interactively. Since then, there has been a paper published to detect cycles, however, there is no way to rank them or ‘play’ with them interactively. This paper is still super awesome and we’re excited there is more work being done in the area!
Our goal is to extract the cycles/holes in a graph, and rank them in order of lowest to highest persistence as a barcode. When a user selects a bar, the cycle will expand and be highlighted in the force-directed layout. All of the nodes/vertices that are a part of this cycle will be constrained together within that cycle, and multiple cycles can be selected at once.
Unlike the 0-d project, we really have no idea what to expect. This project could be a total flop for all we know, but Dr. Rosen told me that’s how new research goes. I’m spending this week converting our work we’ve done on synthetic datasets to some real-world datasets and seeing what we can find. This is definitely some of the hardest work I’ve done to date.