Real Schur Decomposition High Values about cellrank HOT 2 CLOSED

Hi @AlinaKurjan, I think this spectrum looks fine, the range you get for the real part of the top 20 eigenvalues is not unusual. In our initial and terminal states tutorial, the cell number is much smaller (approx. 2500 cells) compared to your dataset, so I would expect your spectrum to be somewhat more "crowded". Keep in mind that the real part has to be between -1 and 1, so the additional eigenvalues from the larger matrix have to go "somewhere".

Your spectrum indicates that 3 or 11 might be good options to test for the number of macrostates. The algorithm would not allow you to compute 2 macrostates, as eigenvalues 2 and 3 are complex conjugates of each other and they want to "stay together"(we describe this more formally in the methods section of the CellRank 1 paper in case you're interested). If you request 2 macrostates, it will automatically compute 3 and give you a warning.

Now, to figure out whether the macrostates you identify with, say n=11 states, are initial, intermediate or terminal, I suggest looking at the coarse-grained transition matrix (see the tutorial I linked above), and using any prior knowledge about the system that you might have. For example, some macrostates might overlap with clusters you have already annotated in your data, and you might know where they reside in the differentiation hierachy. Or you might have experiental time points in your datset, so naturally macrostates with many early-day cells are more likely to represent initial states, etc.

Let me know whether this helps!

from cellrank.

Awesome, thank you for such a detailed reply and it definitely helps! :)

from cellrank.