Efficient algorithms for deriving complete frequent itemsets from frequent closed itemsets

When mining frequent itemsets (abbr. FIs) from dense datasets, it usually produces too many itemsets and results in the mining task to suffer from a very long execution time and high memory consumption. Frequent closed itemset (abbr. FCI) is a compact and lossless representation of FI. Mining FCIs can not only reduce the execution time and memory usage, but also reserve the complete information of FIs derived from FCIs. Although many studies have been proposed with various efficient methods for mining FCIs, few of them have developed algorithms for efficiently deriving FIs from FCIs. In this work, we propose two efficient algorithms named DFI-List and DFI-Growth for efficiently deriving FIs from FCIs. The both algorithms adopt depth-first search and divide-and-conquer methodology to derive all the FIs. DFI-List efficiently derives all the FIs with a vertical index structure called Cid List. DFI-Growth compresses the information of FCIs into tree structures and applies pattern-growth strategy to derive FIs from the trees. Empirical experiments show that DFI-List is the most efficient and scalable algorithm on the dense datasets. For example, when the minimum support threshold is set to 50% on the Chess dataset, DFI-List runs faster than LevelWise (Pasquier et al. Inf Syst 24(1): 25-46, 1999b) over 100 times. As for DFI-Growth, it is the most stable and memory efficient algorithm on the sparse datasets. Both DFI-Growth and DFI-List are superior to the state-of-the-art algorithm (Pasquier et al. Inf Syst 24(1): 25-46, 199b) in terms of execution time.