The Social Web is successfully established, and steadily growing in terms of users, content and services. People generate and consume data in real-time within social networking services, such as Twitter, and increasingly rely upon continuous streams of messages for real-time access to fresh knowledge about current affairs. In this paper, we focus on analyzing social streams in real-time for personalized topic recommendation and discovery. We consider collaborative filtering as an online ranking problem and present Stream Ranking Matrix Factorization -RMFX -, which uses a pairwise approach to matrix factorization in order to optimize the personalized ranking of topics. Our novel approach follows a selective sampling strategy to perform online model updates based on active learning principles, that closely simulates the task of identifying relevant items from a pool of mostly uninteresting ones. RMFX is particularly suitable for large scale applications and experiments on the 476 million Twitter tweets dataset show that our online approach largely outperforms recommendations based on Twitter's global trend, and it is also able to deliver highly competitive Top-N recommendations faster while using less space than Weighted Regularized Matrix Factorization (WRMF), a state-of-the-art matrix factorization technique for Collaborative Filtering, demonstrating the efficacy of our approach.