Collaborative Ranking for Local Preferences

For many collaborative ranking tasks, we have access to relative preferences among subsets of items, but not to global preferences among all items. To address this, we introduce a matrix factorization framework called Collaborative Local Ranking (CLR). We justify CLR by proving a bound on its generalization error, the first such bound for collaborative ranking that we know of. We then derive a simple alternating minimization algorithm and prove that it converges in sublinear time. Lastly, we apply CLR to a novel venue recommendation task and demonstrate that it outperforms state-of-the-art collaborative ranking methods on real-world data sets.