Z-TCA: Fast Algorithm for Triadic Concept Analysis Using Zero-suppressed Decision Diagrams

Abstract

We propose a fast algorithm called Z-TCA for triadic concept analysis (TCA). TCA is an extension of formal concept analysis (FCA), aiming at extracting ontologies by using mathematical order theories from a collection of ternary relations of three groups of variables: the object, attributes, and conditions. It finds various applications in fields like data mining and knowledge representation. However, the state-of-the-art TCA algorithms are suffering from the problem of low efficiency due to the complexity of the task. Attempts have been made to speed up the TCA process using a Binary Decision Diagram (BDD) or its improved version Zero-suppressed Decision Diagram (ZDD), while in this paper, we propose a new way to apply ZDD to TCA, named the Z-TCA algorithm. We conduct experiments on a real-world triadic context built from the IMDb database as well as some randomly-generated contexts and the results show that our Z-TCA algorithm can speed up the TCA process about 3 times compared to the baseline TRIAS algorithm. We also discover that when the density of the context exceeds 5%, our algorithm outperforms all other ZDD-based improved TCA algorithms and becomes the fastest choice for TCA.