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Re: st: similarity statistic for heatmaps (or any cartesian plane)


From   Raymond Lim <rl2240@columbia.edu>
To   statalist@hsphsun2.harvard.edu
Subject   Re: st: similarity statistic for heatmaps (or any cartesian plane)
Date   Wed, 20 Jun 2012 10:26:36 -0400

Thanks for the feedback Nick. Yes, my latter statement is dubious. I
should have said akin to Kolmogorov-Smirnov and not referred to
spatial 1-dimension. Essentially, I want to test whether the
distribution function of two surfaces are statistically different. For
example, say I measure pollution levels in a city in two different
time periods. I want to test whether the distribution of pollution is
the same (I don't care about volume of pollution, just distribution of
it across parts of the city). Alternatively, a correlation measure
would be good too.

Computing the difference between heatmaps sounds like a good start.
Thanks again!

- -
The latter statement is at best dubious and at worst fallacious.

A Kolmogorov-Smirnov test compares distribution functions and says
nothing whatsoever about spatial distribution, as you can shuffle the
locations and keep the same distribution functions. Indeed it wouldn't
surprise me if it were based on an assumption of independent
measurements likely to be challengeable for most interesting spatial
data.

Similarly, you can compare heatmaps aspatially and spatially:
something like concordance correlation compares element by element but
says nothing about spatial patterns. If I were obliged to choose a
single single-number statistic to compare heatmaps it might be
something like a spatial autocorrelation of differences.

But why choose a single statistic any way? Or rather, a map is a
sample statistic, just map-valued, and the best measure of similarity
of two heatmaps may be a heatmap of the difference between them (or,
e.g. their ratio).

Nick

On Tue, Jun 19, 2012 at 4:30 PM, Raymond Lim <rl2240@columbia.edu> wrote:
> Is there a statistic for computing similarity of two heatmaps (or any
> sort of Cartesian plane)? I know in 1 dimension, you can compared
> distributions using a Kolmogorov-Smirnov test, but not sure about
> 2-dimensions.
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