"Goshiwen" <[EMAIL PROTECTED]> wrote in message news:[EMAIL PROTECTED] > > > > I've never given the weighting a great deal of thought, because whenever > > I've used the JS divergence it has made sense for the measure to be > > symmetric (so I choose equal weights). To get the average distribution > just > > take the weighted average of the corresponding probabilities for each > > probability table. e.g. > > > > table1, w1 > > > > (0.4, 0.6) > > > > > > table2, w2 > > > > (0.2, 0.8) > > > > > > average table > > > > (0.4*w1+0.2*w2, 0.6*w1+0.8*w2) > > > > > > What weights will make most sense I can't say, but the measure will AFAIK > > only be symmetric for equal weights. So one question you should ask > > yourself is, "does it make sense for the distance from table1 to table2 to > > be different from the distance from table2 to table1?" > > > > Duncan > > > If I have many samples, and I want to find the average of them in terms of > the distance defined by JS Divergence, it looks like that this average is > NOT the average by Euclidean distance. Is there any proof that they are > same? > > Thanks. > > Goshiwen >
Right, I'm still not 100% sure what you're after. For a given set of probability tables and weights the JS divergence is is simply the entropy of the weighted average table minus the weighted sum of the entropies of the individual tables. It sounds as if you're trying to do something a little out of the ordinary (to me anyway :-)) if you're trying to find some sort of average table on the basis of JS divergence(s). Presumably your average table will be one that minimises / maximises some statistic. If so, what's the statistic? e.g. Are you wanting to find the set of weights (and thus average table) that minimises the generalised JS divergence? Maybe the following links will be of some help. http://www.mtm.ufsc.br/~taneja/book/book.html http://www.mai.liu.se/~tikos/kurser/TAMS23/lindiv.pdf Duncan . . ================================================================= Instructions for joining and leaving this list, remarks about the problem of INAPPROPRIATE MESSAGES, and archives are available at: . http://jse.stat.ncsu.edu/ . =================================================================
