I'm looking for metrics of the degree of grouping/clustering of spatial data. I'm not looking to formally cluster the data i.e. classify points within groupings. But rather an index such as from 0 for a uniform distribution to 1 for a set of spatially coinciding points. All metrics I've seen so far either relate to distributions from the mean or validation of classified clusters. I need something agnostic from any formal groupings, and which works with 2d data (although I'm guessing the solution could also work with 1d data). Grateful for any pointers.
There is e.g. Hopkins statistic of clustering tendency.
But in my opinion these statistics are useless. Let me explain.
Essentially, these statistics usually are a very weak hypothesis test, with H0 being "my data is uniform distributed".
But a data may be clearly not uniform, but nevertheless not "clustering" in the usual sense. For example, a single Gaussian distribution will fail these tests, but not cluster with any algorithm.
Any data set can be made "clustered" by applying
exp to one attribute.
The assumption not uniform $\Rightarrow$ clustered is too simple.
What you are really interested in is whether the data is multi modal rather than unimodal. A better test would therefore try to prove unimodality. But I don't know any.