I want to perform quadrat count analysis on several point processes (or one marked point process), to then apply some dimensionality reduction techniques.

The marks are not identically distributed, i.e., some marks are appearing quite often, and some are pretty rare. Thus, I cannot simply divide my 2D space in a regular grid, because the more frequent marks will "overwhelm" the lesser frequent ones, masking their appearance.

Thus, I tried to build my grid such that each cell has at most N points in it (to do so, I simply divide each cell in four smaller (and equally sized) cells, recursively, until no cell has more than N points in it).

What do you think of this "normalization" technique? Is there a standard way to do such things?

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    $\begingroup$ If you use a regular grid and the more frequent marks outnumber the less frequent ones, I don't see how that "overwhelms" and "masks" things. Could you elaborate a bit? Are you trying to replace each quadrat's contents with only the most common mark, or something like that? $\endgroup$ – Wayne Jul 25 '12 at 18:59

I have used quadrat analysis only on regular grids. It was helpful in regard to the purpose, which was to compare the dispersion of sampling data with a known process, e.g., random. Therefore a regular grid worked well.
The method you developed and described is not sure to be quadrat counting. For example in the moving average method, one option is to count the number of neighbors for the process, i.e., averaging, which is simply done by searching within a circle (in 2D) or sphere (in 3D). Your method looks similar with a slightly different use of those selected samples.

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