In article ,
Jim Menegay  wrote:
>lbrtchx{at}hotmail.com (Albretch) wrote in message
>news:...
>>  Then, given a number of nested sets, how would you define a 'metric'
>> that would measurably give you the distance between any two pairs of
>> them?
>
>Is this a typo?  Do you want a "distance" between two sets, or between
>"two pairs" of sets?

Yes, I think it would be between two nested sets, not two pairs of them.

>The best metric will depend on the properties you want your distance to 
>have.  Is it desirable that the distance between two sets not change as
>more sets are added to the "database"?  The metrics that Joe
F. suggests
>will not have this kind of "stability" (nor should they).

The nested sets referred to are, if I understand properly, each trees.
So the tree distances I discussed are relevant, and would not change as more
trees (nested sets) are added.

>If you want a metric that gives the same answer as more data becomes
>available, then there is really only one metric worth considering - the
>distance is the size of the symetric difference between the two sets.

As these nested sets are not just single sets, but are nested sets of
objects (i.e. hierarchies), the symmetric distance of sets is not the
answer of itself.

-- 
Joe Felsenstein         joe{at}removethispart.gs.washington.edu
 Department of Genome Sciences and Department of Biology,
 University of Washington, Box 357730, Seattle, WA 98195-7730 USA
---
þ RIMEGate(tm)/RGXPost V1.14 at BBSWORLD * Info{at}bbsworld.com

---
 * RIMEGate(tm)V10.2áÿ* RelayNet(tm) NNTP Gateway * MoonDog BBS
 * RgateImp.MoonDog.BBS at 4/7/04 3:31:16 PM