Collaborative filtering Cost Function

I have watched video several and i understand the concept but im getting confused with the formula ,

Can someone please help me with formula and its notations

Thank you

Which notations do you need help with?

why do we remove ‘m’ from formula ? , rest understood the formula :+1:

Hello @Dravid_Vaishnav,

I don’t know exactly why the lecture did that. However, we can analyze it.

If we get rid of the m's, all user-movie pairs are treated equally in front of the cost. All w's are regularized in the same way.

If we keep the m‘s, then those user-movie pairs rated by (active) users who have rated more will be down-weighted more, because the \frac{1}{m} shrinks their importance in the cost function. In contrast, active users’ w's will be regularized less because \frac{\lambda}{m} becomes smaller.

Now, do we think shrinking the effect of ratings by more active user a good way? Would active user’s ratings more reliable in general? Maybe, or maybe not. It depends on the problem you are facing, and so this is to be told by experimentation, and your understanding of the problem you are facing. Perhaps we leave it open as options but keep in mind that the lecture suggested that we can remove them, and then when you work on your own problem, you can think about this again, experiment both, and find yourself your answer.



Don’t need the 1/m, because m is a constant, that just scales the value of the cost. It doesn’t have any impact on the weights that give the mimimum cost.

1 Like