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

complete.

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,

boxes?).

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

noodles.

While I sense I will be killed on this question: Any thoughts or suggested

reading appreciated so I might address more intelligently anon.

Chris

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