LCM: An Efficient Algorithm for Enumerating Frequent Closed Item Sets

In this paper, we propose three algorithms LCMfreq, LCM, and LCMmax for mining all frequent sets, frequent closed item sets, and maximal frequent sets, respectively, from transaction databases. The main theoretical contribution is that we construct treeshaped transversal routes composed of only frequent closed item sets, which is induced by a parent-child relationship defined on frequent closed item sets. By traversing the route in a depth-first manner, LCM finds all frequent closed item sets in polynomial time per item set, without storing previously obtained closed item sets in memory. Moreover, we introduce several algorithmic techniques using the sparse and dense structures of input data. Algorithms for enumerating all frequent item sets and maximal frequent item sets are obtained from LCM as its variants. By computational experiments on real world and synthetic databases to compare their performance to the previous algorithms, we found that our algorithms are fast on large real world datasets with natural distributions such as KDD-cup2000 datasets, and many other synthetic databases.