Association rules are traditionally designed to capture statistical relationship among itemsets in a given database. To additionally capture the quantitative association knowledge, F.Korn et al recently proposed a paradigm named Ratio Rules for quantifiable data mining. However, their approach is mainly based on Principle Component Analysis (PCA) and as a result, it cannot guarantee that the ratio coefficient is non-negative. This may lead to serious problems in the rules' application. In this paper, we propose a new method, called Principal Sparse Non-Negative Matrix Factorization (PSNMF), for learning the associations between itemsets in the form of Ratio Rules. In addition, we provide a support measurement to weigh the importance of each rule for the entire dataset.