Simultaneous mining of frequent closed itemsets and their generators: Foundation and algorithm

• We proposed GENCLOSE to simultaneously mine generators and frequent closed itemsets.
• A necessary and sufficient condition is applied to find generators.
• Three extension operators are used to determine frequent closed itemsets.
• The correctness of GENCLOSE is proven reliably.
• Extensive experiments show that GENCLOSE outperforms existing well-known algorithms.

Closed itemsets and their generators play an important role in frequent itemset and association rule mining. They allow a lossless representation of all frequent itemsets and association rules and facilitate mining. Some recent approaches discover frequent closed itemsets and generators separately. The Close algorithm mines them simultaneously but it needs to scan the database many times. Based on the properties and relationships of closed itemsets and generators, this study proposes GENCLOSE, an efficient algorithm for mining frequent closed itemsets and generators simultaneously. The level-wise search over an ItemsetObject–setGenerator–Tree enumerates the generators by using a necessary and sufficient condition to produce (i+1)-item generators from i-item generators. This condition, based on transaction (object) sets that can be efficiently implemented using diffsets, is very convenient and reliably proved. In the search, pre-closed itemsets are gradually extended using three proposed extension operators. It is shown that these itemsets produce the expected closed itemsets. Extensive experiments on many benchmark databases confirm the efficiency of the proposed approach.