e-NFIS: Efficient negative frequent itemsets mining only based on positive ones

Negative association rules (NAR) mining, which has played important roles in real applications, mainly focuses on the form A⇒B, A⇒¬B, ¬A⇒B and ¬A⇒¬B so far, where A (e.g. (a₁a₂)) and B (e.g. (b₁b₂)) are occurring itemsets. Another form of negative association rules, such as a₁¬a₂⇒b₁¬b₂, which contain occurring (or positive) items and non-occurring (or negative) items, can also reflect the relations of itemsets from another angle. The first step to mine this form of NAR is to mine negative frequent itemsets (NFIS). This paper mainly focuses on this step and proposes a novel method, e-NFIS (efficient negative frequent itemsets), to mine NFIS. The main idea of e-NFIS is to mine NFIS only from positive frequent itemsets (PFIS). E-NFIS contains three aspects: 1) using traditional method to mine PFIS; 2) an efficient method to generate negative candidate itemsets from PFIS; 3) calculate the support of negative candidate itemsets only using the support of PFIS, without additional database scanning. Experimental results show that the e-NFIS is efficient.