Expiring Page Rank algorithm

Question

I'm looking for an algorithm that does some sort of page ranking, but gives less value to pages as they get older.

All algorithms I have seen do the opposite (give older domains more value).

Help finding such an algorithm would be much appreciated.

Edit: Looking at my initial question I think I was a bit unclear as to what I was asking, and the question is more complicated than I originally thought. Basically what I want is some sort of ranking algorithm that if Site A has linked to Site B immediately after site B has made a post, then site B's page gets extra page rank (maybe score is a better word), but if site A has linked to site B a long time after the post has been made, it adds very little to the page rank.

Hopefully this makes sense. Apologies for the initial question being wrong.

It's better to present algorithm which you try it but you can't change it from oldest date to newest date. — Saeed Amiri, Sep 21 '11 at 09:18
@SaeedAmiri: The OP explicitly mentioning the algorithm he's using: pagerank. This problem is clear and a well known for anyone who is familiar with this algorithm. — amit, Sep 21 '11 at 09:29
@amit, I know pagerank but it has some variations, and OP doesn't mentioned that why he can't use it (with a small variation) to use newest posts. — Saeed Amiri, Sep 21 '11 at 09:59
@amit, As I see OP's comment in your answer it seems he isn't familiar with algorithm, so it's better he show us his try then try to use our help. — Saeed Amiri, Sep 21 '11 at 10:03
I don't have to use Page Rank but it's where I'm currently at in a series of investigations. I'm happy for any other suggestions. — user956400, Sep 21 '11 at 14:12

score 5 · Accepted Answer · edited Sep 21 '11 at 11:42

You can use biased page rank, as described by Haveliwala in this article.

The idea is simple, instead of using a regular random component: [1/n,1/n,....,1/n], use a biased random component, and when you take a random walk, instead of going to each page with probability 1/n, go to each page with probability f(doc), where f(doc) is higher for newer pages, and Sigma(f(doc)) = 1 [for all the docs in the collection, so your random component will be [f(doc1),f(doc2),...,f(docn)]

Note that for each document a must is f(doc)>0, otherwise convergence is not guaranteed [the Perron-Frobenius theorem won't apply].

Another possibility is calculating regular page rank, and multiplying it with a different function g:Collection->R that gives a numerical value to each page, and the newer the page is, the higher the score is for this document.

EDIT:
As response to the original question's edit:
Another possibility is when generating the graph for the web, add additional information w:E->[0,1], meaning: add a weight function for each edge, dentoing how important it is, If the link was made shortly after the original edit, w(e) will be closer to 1, and if it is much later, the score will be closer to 0.

When creating the matrix you calculate pagerank on, put Matrix[v1][v2] <- w((v1,v2)), instead of a simple binary value indicating the edge exists in the graph.
Once you have this matrix, calculate PageRank normally.

Sorry I'm reading the paper now and trying to understand it, is this still relevant for the new edited question? — user956400, Sep 21 '11 at 09:31
@user956400: look at my edit: I think it might fit better your editted question. — amit, Sep 21 '11 at 09:41
That sounds easier didn't really realize page rank could be used on non binary data. — user956400, Sep 21 '11 at 14:14
Good answer, though on first reading it seems to imply that pagerank is computed using a random walk, which isn't the case. — Nick Johnson, Sep 22 '11 at 01:10

Expiring Page Rank algorithm

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