  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.
