On the non-redundant representation of the minimax basis of strong associations

Associative rules are the type of dependencies between data that reflect which features or events occur together and how often this happens. Strong associative rules are of interest for those applications where a high degree of confidence of dependencies is required. For example, they are used in information security, computer network analysis and medicine. Excessively large number of identified rules significantly complicates their expert analysis and application. To reduce the severity of this problem, we propose the MClose algorithm, which extends the capabilities of the well-known algorithm Close. The Close algorithm forms a minimax basis in which each strong associative rule has a minimum premise and a maximal consequence. However, in the minimax basis, some redundant strong associative rules remain. The MClose algorithm recognizes and eliminates them in the process of constructing a minimax basis. The proposed algorithm is based on the properties of closed sets. Its correctness is proved by proving the reflexivity, additivity, projectivity, and transitivity properties of strong associative rules.