Mining ratio rules via principal sparse non-negative matrix factorization

Association rules are traditionally designed to capture statistical relationship among itemsets in a given database. To additionally capture the quantitative association knowledge, Korn et al. (1998) 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 nonnegative. This may lead to serious problems in the rules´ application. In this paper, we propose a method, called principal sparse nonnegative 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.