Frequent itemset (FI) mining is an interesting data mining task. Instead of directly mining the FIs from data it is preferred to mine only the closed frequent itemsets (CFIs) first and then extract the FIs for each CFI. However, some algorithms require the generators for each CFI in order to extract the FIs, leading to an extra cost. In this paper, we introduce an effective algorithm, called NUCLEAR, which can induce the FIs from the lattice of CFIs without the need of the generators. It can enumerate generators as well by similar fashion. Experimental results showed that NUCLEAR is effective as compared to previous studies, especially, the time for extracting the FIs is usually much smaller than that for mining the CFIs.

Frequent itemset (FI) mining is an interesting data mining task. Directly mining the FIs from data often requires lots of time and memory, and should be avoided in many cases. A more preferred approach is to mine only the frequent closed itemsets (FCIs) first and then extract the FIs for each FCI because the number of FCIs is usually much less than that of the FIs. However, some algorithms require the generators for each FCI to extract the FIs, leading to an extra cost. In this paper, based on the concepts of "kernel set" and "extendable set", we introduce the NUCLEAR algorithm which easily and quickly induces the FIs from the lattice of FCIs without the need of the generators. Experimental results showed that NUCLEAR is effective as compared to previous studies, especially, the time for extracting the FIs is usually much smaller than that for mining the FCIs.