I see that you're looking for clusters within PCA projections -- You should look for deeper structure with hot new dimensional reduction algorithms, like PaCMAP or LocalMAP!
I've been working on a project related to a sensemaking tool called Pol.is [1], but reprojecting its wiki survey data with these new algorithms instead of PCA, and it's amazing what new insight it uncovers with these new algorithms!
Thanks for pointing those out — I hadn’t seen PaCMAP or LocalMAP before, but that definitely looks like the kind of structure-preserving approach that would fit this data better than PCA. Appreciate the nudge — going to dig into those a bit more.
Ooooo I will definitely check it out! It's strangely hard to find any comparisons in youtube videos -- it seems TDA isn't actually a dimensional reduction algorithm, but something closely relayed, maybe?
PaCMAP (and its descendant localmap) are comparable to t-sne at preserving both local and global structure (but without messing much with finicky hyperparameters)
I've been working on a project related to a sensemaking tool called Pol.is [1], but reprojecting its wiki survey data with these new algorithms instead of PCA, and it's amazing what new insight it uncovers with these new algorithms!
https://patcon.github.io/polislike-opinion-map-painting/
Painted groups: https://t.co/734qNlMdeh
(Sorry, only really works on desktop)
[1]: https://www.technologyreview.com/2025/04/15/1115125/a-small-...