Input to the "interaction linear model" about ncem HOT 2 CLOSED

We formulated the methods section in our manuscript in the most general way. The interactions can indeed be $X^I \in \mathbb{R}^{N \times L}$, but let be be more precise:

1. Generally it holds that $\mathbb{N} \subset \mathbb{R}$. In the ncem manuscript we tried to be as flexible as possible and in theory the framework would also allow passing non discrete cell types and replacing them with rather cell states or transitions between cell types or proportions/abundances of cell types in e.g. Visium spots. In this case, it would clearly hold that $X^L \in \mathbb{R}^{N \times L}$.

2. For an un-scaled adjacency matrix one will have $A \in \mathbb{1}^{N \times N}$ and $X^L \in \mathbb{1}^{N \times L}$ which results in an interaction matrix of the form $X^I \in \mathbb{N}^{N \times L}$ and again $\mathbb{N} \subset \mathbb{R}$. But ncem also incorporates the option to leverage a scaled adjacency matrix of the form $A \in \mathbb{R}^{N \times N}$. In this case, one obtains an interaction matrix of the form $X^I \in \mathbb{R}^{N \times L}$

I hope this helps to understand the udnerlying concept and why the manuscript methods are phrased more generally.

from ncem.

I am closing this issue, but feel free to open it again in case of further questions on the underlying methods.

from ncem.