[R] discrete entropy is not rotation invariant?
mobygeek at yahoo.com
Mon Mar 20 02:58:58 CET 2006
suppose one is forming a probability p(x,y), where the
axes are somewhat accidental and rotation is possible.
I'm thinking about whether the discrete entropy H(x,y)
if the probability is rotated in the x,y plane.
My current conclusion is that it _does_ change, at
least if the
entropy is estimated via bins. As a simple example,
the probability mass is concentrated in a single bin
(that is not
close to the center of rotation), but it is not a true
After rotation, the probability mass will often be
spread into two bins,
simply because it does not exactly align into one bin.
changes the estimated entropy.
My question: should one regard this as an artifact of
or is it correct to consider that the entropy changes?
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