Q:

I'm studing your article as part of the degree seminarion, and found unclear math calculation on section 3.4

There is a formula to handle bias terms where you replace bias for item j, by substracting the maximun bias of item k.
This math should result with lower than zero value for the new bias?


A:

We want the new biases to be negative (without changing the ranking for any queries in any way) so that we can take the square root of the negated value (for L2 distance). You can easily verify that our new equation is equivalent to Eq. (1) with bias term absorbed.