Matrix approximation (MA) is one of the most popular techniques for collaborative filtering (CF). Most existing MA methods train user/item latent factors based on a user-item rating matrix and then use the global latent factors to model all users/items. However, globally optimized latent factors may not reflect the unique interests shared among only subsets of users/items, without which unique interests of users may not be accurately modelled. As a result, existing MA methods, which cannot capture the uniqueness of different user/item, cannot provide optimal recommendation. In this paper, a mixture probabilistic matrix approximation (MPMA) method is proposed, which unifies globally optimized user/item feature vectors (on the entire rating matrix) and locally optimized user/item feature vectors (on subsets of user/item ratings) to improve recommendation accuracy. More specifically, in MPMA, a method is developed to find both globally and locally optimized user/item feature vectors. Then, a Gaussian mixture model is adopted to combine global predictions and local predictions to produce accurate rating predictions. Experimental study using MovieLens and Netflix datasets demonstrates that MPMA outperforms five state-of-the-art MA based CF methods in recommendation accuracy with good scalability.