Converting a formula into PHP

Question

I'm trying to convert this adaptive bayesian rating formula into PHP code: see here.

Here are the details of the various parts of the formula..

• nvotes : total number of votes so far
• nlinks : total number of links
• nvotes(k) : number of votes cast to rth link.
• deltarank(k, m) : rank increment caused by kth vote that is casted to mth link.
• nsaves(i) : number of users that save ith link to their linkibol.
• a : save exponent (an ad-hoc value close to 1)
• age(i) : the difference (in days) between date link added and current date.
• b : decay exponent (an ad-hoc value close to 0)

(full details of the formula can be found at http://blog.linkibol.com/2010/05/07/how-to-build-a-popularity-algorithm-you-can-be-proud-of/ - scroll down to the "How Do We Implement Popularity in linkibol?" section)

I can convert most of this function into PHP code easily, but the bit I'm not understanding is the sigma and deltarank bit. I'm not sure what that bit is supposed to do or what values to pass to k and m.

If anyone has any tips or could break the complex bit of the formula down that'd be great, then I can look at what would be the best way to implement it in PHP - there might be functions I could make use of etc..

Answer 1

The sigma part is summation. Use the values provided as the loop counter. (so k=1 to 10, use those values in the functions that take k).

Delta is simply a difference, but that particular function surely has a more precise definition.

Answer 2

They define the delta rank as the change in rank when the kth vote is cast on the mth link... it seems like that's arbitrary, since their rank change is based on the karma of the users casting the vote.

As for the sigma, it's just the sum of the contents from (k=1) to (k=whatever), so you'll implement that with a loop.