Handling Large Formal Context Using BDD --- Perspectives and Limitations

Authors:
Andrei Rimsa;Luis E. Zárate;Mark A. Song
Affiliations:
Department of Computer Science, Applied Computational Intelligence Laboratory, Pontifical Catholic University of Minas Gerais, Brazil;Department of Computer Science, Applied Computational Intelligence Laboratory, Pontifical Catholic University of Minas Gerais, Brazil;Department of Computer Science, Applied Computational Intelligence Laboratory, Pontifical Catholic University of Minas Gerais, Brazil
Venue:
ICFCA '09 Proceedings of the 7th International Conference on Formal Concept Analysis
Year:
2009

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Abstract

This paper presents Binary Decision Diagrams (BDDs) applied to Formal Concept Analysis (FCA). The aim is to increase the FCA capability to handle large formal contexts. The main idea is to represent formal context using BDDs for later extraction of the set of all formal concepts from this implicit representation. BDDs have been evaluated based on several types of randomly generated synthetic contexts and on density variations in two distinct occasions: (1) computational resources required to build the formal contexts in BDD; and (2) to extract all concepts from it. Although BDDs have had fewer advantages in terms of memory consumption for representing formal contexts, it has true potential when all concepts are extracted. In this work, it is shown that BDDs could be used to deal with large formal contexts especially when those have few attributes and many objects. To overcome the limitations of having contexts with fewer attributes, one could consider vertical partitions of the context to be used with distributed FCA algorithms based on BDDs.