Re: spatial autocorelation methods

From: Fred Marshall (fmarshallx_at_remove_the_x.acm.org)
Date: 10/12/04 

Date: Tue, 12 Oct 2004 16:40:48 -0700

"Ara.T.Howard" <Ara.T.Howard@noaa.gov> wrote in message
news:Pine.LNX.4.60.0410121555140.13675@harp.ngdc.noaa.gov...
>
> i'm facing a problem where i need to do some spacial autocorelation on
> some
> data. the problem is that all the methods i've found (moran's i, k-means,
> etc.) work on rectangular input data sets with no notion of 'missing'.
> what i
> have is a rectangle with some data and some missing and need to run
> whatever
> calculation i end up using in a way that does not factor in the missing
> data.
> is anyone out there aware of algorithims or, better, code which might to
> this?

Is the data subject to lateral movement? Or, are the positions fixed and
you just have new data sets and are trying to find the best match?

2-D correlation is the same as 1-D correlation but with a double integral -
which you might envision as a raster scan with different degrees of overlap
perpendicular to the raster scan direction - if the coordinate system is
rectangular. No matter what it's still multiply and integrate (i.e.
accumulate) at each value of offset. So, if there's no lateral motion
involved then there's no need to look at offset registration and you do a
single zero-valued offset multiply and integrate.

As far as missing data is concerned, there would be a couple of issues:
- ignoring those coordinates
- weighting for the loss of inputs to the integration.
Assume that there is a grid for NxN data points and that the number of
missing data points is [I J K L M .... ]

The potential sum of unit samples is N^2. If the real potential sum is
N^2-I, N^2-J, ... etc. then I think you might weight the results by
N^2/[N^2-m] where m is the number of missing points for each integration -
so that a plane of unit samples (with some missing) will always have a
weighted integral of N^2. The same applies if you have to shift the data
and compute multiple points of the correlation function and you might treat
the nonoverlapping areas the same way - as "missing". If you do, then the
edges will be noisy!! So, maybe it's better to let the nonoverlap be zeros.

All this is just logical to me - no special knowledge on my part.

Fred

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