alpha hulls (always complete) and incomplete envelops (confidence intervals)
I have a series of noodles, which is to say line shapes, that I am trying
to come to grips.
If I generalize these lines away to point clouds in time order, then an
alpha hull will contain all points, as would convex hull, but potentially
with less wasted space. The thing about a convex hull or alpha hull is that
all samples are 'within'. This is to say that it is converged as sample =
infinity, or, more normally, sample = total number of samples available
which is generally less than infinity.
In a very general way, I am wondering if there is an accepted method to
allow, say 30 percent of the 'alpha hulled' samples (which clearly are not
designed to allow such) to reside outside the alpha hull (essentially
creating confidence intervals upon the alpha hull (or perhaps I haven't
read enough)) . Secondarily, is there a way to compare 'confidence
interval' alpha hulls, where 70 percent of the sample points reside within,
and the rest exogenous.
I ask as my noodles may share, to an unknown amount, but perhaps
extensively, commonalities of co-existance to as much as 70 percent (it is
speculated) of an alpha hull space, and the variance that I am trying to
account for is the 30 percent that I would guess and perhaps to define as a
separate alpha hull, or some sort space, outside the alpha hull space.
Having it both ways: *if *100% of points are within the alpha hull, how
might one reduce this to 70% or some such, because hulls are always sample
I realize that this probably sounds inchoate, or am I fantabulizing, but I
think I am asking about comparing the shapes of constrained (incomplete)
alpha hulls in the context of Parzen windows (whose shape I wonder about,
Another way of looking at this a point process is that given a 1280x1280
grid, there are an enormous number of cells that will always be NA, a
smaller number that will be visited once. So how to proceed to compare the
While I sense I will be killed on this question: Any thoughts or suggested
reading appreciated so I might address more intelligently anon.