Aligned UMAP: clarification on 'overlapping' points through time?

Hi! Thanks very much for developing these wonderful tools. I've used UMAP for a little while and now I'm very excited to try out Aligned UMAP. The instructions provide an example which is not merely "contrived", it's... hard to see how to use actual time-dependent data.

In the example, we have 10 digits and time evolution is put into 10 time steps (the coincidence of the two different 10's really slowed me down lol), but... somehow you make it so that data points are shared between time steps? I don't see how to adapt that to the (common?) case in which all the data points change at each time step.

It's still not clear to me how we're supposed to build some sort of "overlapping" amount of points. (Are we expected to insert "glue frames" in between our time slices, for which we grab half the points from the previous time and half from the next time?)

My current application is that I have 6 different classes of points, with 360 examples for each class, for which there are vectors that are 64 dimensional and evolve over 512 time steps. I'm ok with downsampling the 512 to, lol, maybe 8 or 16 for starters. But... still the "make them overlap" isn't clear to me -- they all change.

Could someone please clarify? I'd be happy to contribute to the documentation,....once I understand how this is supposed to work.

It is generally the case that the indices of points that are supposed to align will persist from time step to time step. Is there a mode whereby we can can make use of that?

Thanks.

Start with the Aligned UMAP basic usage instructions linked in the issue and compare the example with the described time-dependent data. Clarify how overlapping points or persistent indices should be represented, then update the documentation so users can tell how to handle independently changing points across time steps.