Like describing the density, shape, etc. of point clouds in scatterplots it would also be valuable to have a feature vector that helps estimate interesting properties of high-dimensional datasets. Interesting features that come to my mind: size, intrinsic dimensionality, noise variance, shape of dense regions, etc. At the best case: do you know libraries that provide such 'metadata' about high-dimensional data sets?
A review of methods for estimating data dimensionality: http://www.disco.ethz.ch/lectures/seminar/paper/Samuel/3.pdf
I have never tried using such features as metadata, but I would try looking at the distributions of the distances (not necessarily Euclidean) between your points. This could tell you something about the dense clusters or outliers in the data.
What is your end goal with these features?
Maybe this site helps: http://www.dbs.ifi.lmu.de/cms/ResearchKriegel/Projects
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