Collaborative Filtering (CF) is a well-established method in Recommendation Systems. Recent research focuses on extracting recommendations also based on implicitly gathered information. Implicit Feedback (IF) systems present several new challenges that need to be addressed. This paper reports on MuSIF, a product recommendation system based solely on IF. MuSIF incorporates CF with Matrix Factorization and Association Rule Mining. It implements a hybrid recommendation algorithm in a way that different methods can be used to increase accuracy. In addition, it is equipped with a new method to increase the accuracy of matrix factorization algorithms via initialization of factor vectors, which, as far as we know, is tested for the first time in an implicit model-based CF approach. Moreover, it includes methods for addressing data sparsity, a major issue for many recommendation engines. Evaluation shows that the proposed methodology is promising and can benefit customers and e-shop owners with personalization in real world scenarios.