[Gdal-dev] Parzen Window Kernel Density Filter

[Marek Brudka]

Hi,

Bill Binko wrote:

>3) How much would I need to buffer around the viewable area?  I've been 
>thinking about it, I don't think I need to use all of the points in the 
>dataset, only the viewable area + a buffer for the impact of those points 
>just outside of the area.  I am thinking that I will only need to buffer 
>by, say, 4 times the variance (kernel size) since anything farther than 
>that won't cause much impact... does that sound right?
>  
>
While I did not ever consider to use gaussian mixture densities (Parzen 
Window with gaussian kernel) for the interpolation  of geospatial data, 
I suppose that 4 times the covariance is even more than necessary. 
Usually 3 covariances are enough to neglect the "tails" of gaussian 
density (especially in more than one dimension :-) ).

If I've understood you the well, I suppose that your problem is not from 
a statistics domain but rather from the interpolation one. I assume that 
you are interested in a kind of smooth transition between data in sample 
grid (irregular?) and you do not insist on interpreting the resulting 
function as a probability density.  Did you considered to apply radial 
basis function (RBF) approximators? In fact, if RBF is a gaussian one, 
which is a common case, you have something very similar to Parzen 
Window, but without (unnecessary) probability interpretation.

You question regarding the relation between covariance and scale can be 
nicely answered using classic Shanon sampling theory and spectral 
analysis. I remember one great paper on this

"Sanner, R., and Slotine, J.J.E., "Gaussian Networks for Direct Adaptive 
Control," I.E.E.E. Trans. Neural Networks, 3(6), 1992. (best paper award)"

where you can read a lot about RBF approximations (and adaptive control 
too, but approximation is more important)

HTH

Marek Brudka