Inhomogeneity adjustment in the RDF

[foxojs]

Hi,
I’m using Freud to analyse large scale spatial transcriptomics data. This is essentially a multi type point pattern dataset with c.100million points, each with x,y,z coordinates and a gene label. I am using the RDF to identify pairwise relationships between each of the labelled genes within the data. However, the points themselves show substantial inhomogeneity across the sample (as to be expected with tissue architecture etc). I was wondering if there is a way to adjust for this inhomogeneity in a similar fashion to the pcfcross.inhom function from spatstat? I can’t use spatstat itself as the code is not optimised to deal with rhe 3dimensional and large number of points in a given transcriptomics sample.

Would appreciate anyone’s thoughts or ideas on this, particularly if there’s a way to adapt freud’s RDF directly,

thanks

[joaander]

You can access the bin_counts that freud.density.RDF computes and post process it however you like. freud.density.RDF doesn't work with labelled data directly, you need to pass in the appropriate subsets of your dataset to points and query_points.

[foxojs]

Hi, thanks for the response - My understanding is that the inhomogeneity adjustment (e.g., as in spatstat::pcfcross.inhom) requires per-pair weighting based on local intensity estimates (i.e., weighting each pair by 1 / (λ(x_i) * λ(x_j))) before binning distances. Am I therefore correct in thinking this kind of correction can't be done through RDF directly, and would need a manual implementation. Perhaps through using the ase AABBquery and Gaussian density to compute local estimates of intensity?

[joaander]

CorrelationFunction computes the r-binned averages of $C(r) = \left\langle s^*_1(0) \cdot s_2(r) \right\rangle$ where $s$ is complex. If you set a real-valued $s = 1/\lambda$, you could compute the quantity you are interested in.

Note that CorrelationFunction does not normalize by $V \frac{N-1}{N}$ nor does it compute the number densities in the bins. That part can be included by post processing appropriately using the values provided in bin_counts and bin_centers.

[foxojs]

Ah I see that makes sense - thank you for the help (and for the library, I've enjoyed using it)