Analysed United Nations General Assembly votes over the years using the Kepler Mapper. Computational Topology course project. Presentation slides
Positives: Finally got hands on data analysis experience. Was very happy when it resonated with known historical facts.
Negatives: Not a lot of higher order topology, often making it just a sophisticated clustering algorithm. Actually saw how fishy the work of manually tuning parameters in data analysis can be.
Technical takeaways: Preprocessing data - smoothing out issues systematically in large datasets. Using data analysis tools. Statistically verifying results to make sure parameter tuning didn’t artifically manufacture them.
Meta takeaways: Information hygiene is extremely important in data analysis. Be very vigilant about how you concluded what you think you know. Make sure you have ways to check that you are definitely not observing the result of a different, more ubiquitous probability distribution over your sample space (say, the uniform one).