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Re: Correct way to normalize an rmsd-based distance metric used in
repeated trials of pairs
Posted:
Mar 20, 2012 1:23 PM
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Thanks very much for taking the time - I'm sorry I didn't make myself
clear.
After any given "throw", the "rmsd" is the rmsd for the inter-atomic
distances for the 30 pairs of beads that lie within 1/4 inch of each
other in each trial. (If the "throw" doesn't yield just 30 such
pairs, I ignore the "throw".)
So, when I do 500 "throws", I get 300 in which there are just 30 of
such pairs, and my "average rmsd" is the average of the rmsd's
computed for each of these 300, i.e. an average of 300 individual
rmsds. (Note that each rmsd that figures into this average rmsd was
computed for just 30 pairs.)
And when I do another 1000 "throws", I get 525 in which there are just
30 of such pairs, and my "average rmsd" is the average of the rmsd's
computed for each of these 525, i.e. an average of 525 individual
rmsds. (Again, note that each rmsd that figures into this average
rmsd was computed for just 30 pairs.)
And when I do another 1500 "throws", I get 930 in which there are just
30 of such pairs, and my "average rmsd" is the average of the rmsd's
computed for each of these 930, i.e. an average of 930 indiviudal
rmsds. (Again, note that each rmsd that figures into this average
rmsd was computed for just 30 pairs.)
And when I do another 2000 "throws", I get 1140 in which there are
just 30 of such pairs, and my "average rmsd" is the average of the
rmsd's computed for each of these 1140, i.e. an average of 1130
individual rmsds. (Again, note that each rmsd that figures into this
average rmsd was computed for just 30 pairs.)
And what I was trying to say is that as my "yields" go up from 525 to
930 to 1140, my "average rmsd's" go down, even though each of these
"average rmsd" was computed for a set of rmsd's in which each rmsd was
obtained from measurements on just 30 pairs. (In other words, the
"30" stays constant, even though the throws and the yields increase.)
This has nothing to do with your example, so far as I can tell,
because in every case, the rmsd is always computed for just 30
elements, not an increasing nor decreasing number of elements.
What I believe is happening is that as the number of throws goes up,
the "yields" go up, and as the "yields" go up, there are simply more
ways in which 30 pairs can lie closer, so the "average rmsd's" go
down.
But assuming I'm correct about this, I'm still stuck with my original
question: how would you normalize the average rmsd's relative to the
number of throws (or number of returns in the yields from the throws),
assuming you need to for reasons I won't go into here ?
Again - thanks very much for taking the time ...
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