PaCMAP

I was not aware this existed and it looks cool! I am definitely going to take out some time to explore it further. I have a couple of questions for now: (1) I am confused by your last sentence. It seems you're saying embeddings are a substitute for clustering. My understanding is that you usually apply a clustering algorithm over embeddings - good embeddings just ensure that the grouping produced by the clustering algo "makes sense". (2) Have you tried PaCMAP? I found it to produce high quality and quick results when I tried it. Haven't tried it in a while though - and I vaguely remember that it won't install properly on my machine (a Mac) the last time I had reached out for it. Their group has some new stuff coming out too (on the linked page). [1] https://github.com/YingfanWang/PaCMAP

A lot of relationships are (locally) linear so this isn’t as restrictive as it might seem. Many real-life productionized applications are based on it. Like linear regression, it has its place. T-SNE is good for visualization and for seeing class separation, but in my experience, I haven’t found it to work for me for dimensionality reduction per se (maybe I’m missing something). For me, it’s more of a visualization tool. On that note, there’s a new algorithm that improves on T-SNE called PaCMAP which preserves local and global structures better. https://github.com/YingfanWang/PaCMAP

I'd be really curious to see what happens if you use PaCMAP (https://jmlr.org/papers/volume22/20-1061/20-1061.pdf) and more recent large-scale variants (https://github.com/YingfanWang/PaCMAP).

Check out PaCMAP, AFAIK it’s the current SoTA in dimensionality reduction: https://github.com/YingfanWang/PaCMAP

Just on that UMAP point, I’ve found a lot success using PaCMAP (https://github.com/YingfanWang/PaCMAP) instead, which AFAIK is the SOTA in dimensionality reduction algorithms.