Association analysis using the mining of positive and negative association rules (PNARs) was so far primarily based on mining rules of forms \(A\Rightarrow B\) , \(A \Rightarrow \lnot B\) , \(\lnot A \Rightarrow B\) , and \(\lnot A \Rightarrow \lnot B\) . Most existing algorithms for mining PNARs usually exploit the upward closure property of negative itemsets, while few exploit the downward closure property. PNARs mined by algorithms built in the first exploitation method are not really suitable for human thinking and for explaining association analysis. PNARs mined by algorithms built in the second exploitation method are not intuitively described as the PNARs above. Such rules are consistent with human thinking, but generally, they are just positive and negative dependency relationships. Thus, they are confusing and difficult to understand. So far, no existing algorithm can find all valid PNARs. This work proposes an algorithm based solely on (positive) items in transaction databases under the second exploitation to mine PNARs. The algorithm is developed under the support-confidence framework on equivalence classes. Two steps of the association rule (AR) mining process, discovering frequent itemsets and generating ARs from these itemsets, are executed concurrently. The algorithm is sound and complete. Its computational complexity is also estimated. The experiment shows the application prospect of the proposed algorithm in the association analysis of co-occurrence and non-co-occurrence events.
