Collaborative ranking with a push at the top

The goal of collaborative filtering is to get accurate recommendations at the top of the list for a set of users. From such a perspective, collaborative ranking based formulations with suitable ranking loss functions are natural. While recent literature has explored the idea based on objective functions such as NDCG or Average Precision, such objectives are difficult to optimize directly. In this paper, building on recent advances from the learning to rank literature, we introduce a novel family of collaborative ranking algorithms which focus on accuracy at the top of the list for each user while learning the ranking functions collaboratively. We consider three specific formulations, based on collaborative p-norm push, infinite push, and reverse-height push, and propose efficient optimization methods for learning these models. Experimental results illustrate the value of collaborative ranking, and show that the proposed methods are competitive, usually better than existing popular approaches to personalized recommendation.