A Formal Concept Analysis Approach to Data Mining: The QuICL Algorithm for Fast Iceberg Lattice Construction

Association rule mining (ARM) is the task of identifying meaningful implication rules exhibited in a data set. Most research has focused on extracting frequent item (FI) sets and thus fallen short of the overall ARM objective. The FI miners fail to identify the upper covers that are needed to generate a set of association rules whose size can be readily exploited by an end user. An alternative to FI mining can be found in formal concept analysis (FCA). FCA derives a lattice whose concepts identify closed FI sets and connections identify the upper covers. However, most FCA algorithms construct a complete lattice and therefore include item sets that are not frequent. An iceberg lattice, on the other hand, is a lattice whose concepts contain only FI sets. This paper presents the development of the Quick Iceberg Concept Lattice (QuICL) algorithm. QuICL uses recursion instead of iteration to navigate the lattice and establish connections, thereby eliminating costly processing incurred by past algorithms. The QuICL algorithm was evaluated against a leading FI miner and lattice construction algorithms using cited benchmarks. Results demonstrate that QuICL provides performance on the order of FI miners yet additionally derive the upper covers. Beyond this, QuICL has proved to be very efficient, providing an order of magnitude gains over other lattice construction algorithms.