Collaborative Filtering with Stability

Collaborative filtering (CF) is a popular technique in today's recommender systems, and matrix approximation-based CF methods have achieved great success in both rating prediction and top-N recommendation tasks. However, real-world user-item rating matrices are typically sparse, incomplete and noisy, which introduce challenges to the algorithm stability of matrix approximation, i.e., small changes in the training data may significantly change the models. As a result, existing matrix approximation solutions yield low generalization performance, exhibiting high error variance on the training data, and minimizing the training error may not guarantee error reduction on the test data. This paper investigates the algorithm stability problem of matrix approximation methods and how to achieve stable collaborative filtering via stable matrix approximation. We present a new algorithm design framework, which (1) introduces new optimization objectives to guide stable matrix approximation algorithm design, and (2) solves the optimization problem to obtain stable approximation solutions with good generalization performance. Experimental results on real-world datasets demonstrate that the proposed method can achieve better accuracy compared with state-of-the-art matrix approximation methods and ensemble methods in both rating prediction and top-N recommendation tasks.