Consider collaborative filtering problem. We have matrix $M$ of size #users * #items. $M_{i,j} = 1$ if user i likes item j, $M_{i,j} = 0$ if user i dislikes item j and $M_{i,j}=?$ if there is no data about (i,j) pair. We want to predict $M_{i,j}$ for future user, item pairs.
Standard collaborative filtering approach is to represent M as product of 2 matrices $U \times V$ such that $||M – U \times V||_2$ is minimal (e.g. minimizing mean square error for known elements of $M$).
To me logistic loss function seems more suitable, why are all algorithms using MSE?
Best Answer
We use logistic loss for implicit matrix factorization at Spotify in the context of music recommendations (using play counts). We've just published a paper on our method in an upcoming NIPS 2014 workshop. The paper is titled Logistic Matrix Factorization for Implicit Feedback Data and can be found here http://stanford.edu/~rezab/nips2014workshop/submits/logmat.pdf
Code for the paper can be found on my Github https://github.com/MrChrisJohnson/logistic-mf