While you make the utility of converting a multiset to a bet fit power curve pretty clear, I can’t think of actual examples of converting power curves into multisets.

If we consider, as I was suggesting, the weight of the tags as the number of people who have used a tag divided by the number of people who have bookmarked the url, then the size (i.e. the weight) does indeed approaches zero. Using the weight, instead of the actual number is important to rinormalise the distance between different urls and make them comparable. If you have two urls which has exactly the same ratio among the tags, but one has been bookmarked double the amount of time then the other, the distance between the position in the hipercube of the weight would be zero. Instead the distance between the one bookmarked more and the one bookmarked less is bigger than zero, and exactly equal to the distance between the one bookmarked less and the origin of the coordinates.

In other words: you have to use the weight (or other rinormalization techniques). It does make a fundamental difference.

Thank you Ben, from you is worth double.

Yes, I had to cut the long tail. But this was not for space limitation but because at the time I had no ready made software to screen scrape delicious. And I would agree that the whole info is extreemly interesting. Especially if we want to calculate the distance between two URL the exact shape of the tail might as important as the main tags. But this will depend upon the metric chosen.

On the other hand I really think that it does not make much sense to just list all the tags, unordered (or ordered alphabetically). As time goes to infinity I suspect that each and every word might appear; each and every grammatical error, too (del.iciou.s as well as delifious). But we shouldn’t think that those tags would all appear with the same frequency epsilon. They will be diversified, too. And this differenziation might give insights too, thus the importance of the long tail expressed before.

But if we just list all the tags we would, at the limit, just list every alphanumeric string. All the info would be gone.

One point I think it worth finding a niche for: consider your example page. It has lots and lots of tags that aren’t shown in the summary (presumably so the UI doesn’t become overwhelming). Tags like test, maps, words in foreign languages, etc. Given the power-law nature of this a surprising proportion of the volume of the tag set is found in these. Then there are all those people who posted it who presumably had tags on the tip of their fingers yearning to break free. Here’s a posting that shows all the tags for a URL. I found it fascinating.

Truncating the tail of power-law distributions has consequences.

P.S.: » On Tag Clouds, Metric, Tag Sets and Power Laws ell, the idea of passing tag c [...]

Company: Consumating
Launched: 2005
Location: Austin, TX
Overview:

Consumating is dating 2.0. Yes, it’s dating with tags. They also use a bit of Ajax in their interface.
After registering (it’s free), you create an online profile. The …