stephenbrooks.orgForumMuon1GeneralTop250 parameter distribution problem
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Bananeweizen
2002-08-15 12:36:22
Hello all !

Today I investigated the top250 file in the advanced mode of the result viewer.  I set x as zero, y as a certain parameter and z as the percent muon yield.  So one can investigate the dependencies between the muon yield and each single parameter.
By browsing through the parameter list I found the following fact: As one would suspect there are often some slightly different results near each other.  This is what we expect from the optimizer as it tries to slightly change "good" results.  But another thing I can't understand: Those slightly different results are nearly always placed along a line (which is parallel to the z axis) in the resultviewer.  This means that all results of such a "result line" do have the _exact_ same parameter value for the selected parameter.  From my point of view (and what I read about the genetic optimization) I would expect that those nearly equal results are not placed along a line but are grouped in small clouds/clusters where also slightly higher or slightly lower parameter values occur.

On first thought I only saw two possibilities to explain this: The first one would be some kind of bug in the display routines of the viewer.  The second one is about the genetic optimization.  In one of four runs it tries to select a random point on a line just between two good results.  Maybe this technique leads to such "result lines".

Can somebody explain this phenomenon to me or is there just a big fault in my thoughts?

Ciao, Michael.

www.Rechenkraft.de - the most comprehensive german website about internet based distributed computing projects.
Stephen Brooks
2002-08-15 13:10:44
The problem is that the space is 137-dimensional, meaning that 3-dimensional or 2-dimensional projections can be misleading.  I think if you were to plot the results in a projection where all 137 axes were counted for, you'd see that the ones that lie along "lines" actually differ in other parameters.  Consider the 137 vectors

[ 1 0 0 0 ... 0 0 ]

[ 0 1 0 0 ... 0 0 ]

...

[ 0 0 0 0 ... 0 1 ]

Now these are all a distance 1.414 from each other in 137-dimensional space, and yet in any projection onto 3 axes, 134 of them would appear to be in exactly the same place!

The optimiser certainly does produce lines due to that optimisation, but if the yield is still going up it must be working.


"As every 11-year-old kid knows, if you concentrate enough Van-der-Graff generators and expensive special effects in one place, you create a spiral space-time whirly thing, AND an interesting plotline"
scottsaxman
2002-08-15 14:31:12
137 dimensions?  Is there a list somewhere of them all?

-edit- So, after doing some searching and reading, again, things aren't as simple as they might seem.  But, then, anyone who knew there were 137 dimensions knew that already.  As it turns out, I read some stuff about 133 (137 minus the 4 everyday sort of dimensions) that I found more personally interesting, so I'll stick with that.

When did science get so blasted complicated?  smile

[This message was edited by scottsaxman on 2002-Aug-15 at 22:10.]
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