All-to-All distances for point pattern analysis

Question

I am new to point pattern analysis. Trough my readings I haven't seen that any book would suggest to use All-to-All distances for point pattern analysis, but rather they talk about NND or other second order characteristics (K function or pair correlations, etc.). Therefore, I have a naive question why All-to-All is not promoted for point pattern analysis (like cluster detection)?

Thank you!

edit: Imagine one has 100 point patterns, that were experimentally observed (each observation has a specific window). One can compute all pairwise distances for these patterns and compute pairwise distances for uniformly distributed points in the corresponding windows. Then, one can look at the cumulative distributions of these pairwise distances (attached figure).

By accomplishing KS test one can conclude that those distributions are different, therefore observed data was not generated by "random" process. Do you think this test is sufficient?

I am afraid that due to the variability within the observed data, it can be not a trustworthy approach.

Answer 1

I assume All-to-All means all the pairwise distances between the points of a point pattern. These are certainly used since e.g. Ripley's K-function is a sensibly constructed summary of the point pattern based exactly on all the pairwise distances. I suggest you have a look at the free sample chapter 7 of our book Spatial Point Patterns: Methodology and Applications with R which you can download at the book website: http://book.spatstat.org/ In particular section 7.3.1 about the empirical K-function starts with considering all pairwise distances between points.