Inverse distance weighted interpolation for categorical and/or binary datasets

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I want to perform an Inverse distance weighted (IDW) interpolation to a series of points. However my data set can be categorical or binary and just like the IDW I want to interpolate the new values (categorical or binary) based on the highest frequency of closest points values surrounding the prediction location:

A if the majority of the closest points are A

C if the majority of the closest points are C

...

In addition I want to avoid using close points that are behind a barrier, that can be a wall or just an elevation.

This is how the problem/dataset looks like:


The grey points is the point I want to interpolate and the points behind the barriers can't be used in the process. The output of the interpolation process would be A or B, in this case probably A, since the closest points are all A.

What I am looking for is some kind of work-flow that would allow me to do this in ArcGIS, if possible I would prefer R (if anyone has any experience in doing this kind of processes in R). This is just the example how my problem looks like, I still have to implement it to a bigger extent and to many layers of points. Bear in mind that I have little experience with interpolation.



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