A Partial-Closure Canonicity Test to Increase the Efficiency of CbO-Type Algorithms

  • Simon AndrewsEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8577)


Computing formal concepts is a fundamental part of Formal Concept Analysis and the design of increasingly efficient algorithms to carry out this task is a continuing strand of FCA research. Most approaches suffer from the repeated computation of the same formal concepts and, initially, algorithms concentrated on efficient searches through already computed results to detect these repeats, until the so-called canonicity test was introduced. The canonicity test meant that it was sufficient to examine the attributes of a computed concept to determine its newness: searching through previously computed concepts was no longer necessary. The employment of this test in Close-by-One type algorithms has proved to be highly effective. The typical CbO approach is to compute a concept and then test its canonicity. This paper describes a more efficient approach, whereby a concept need only be partially computed in order to carry out the test. Only if it passes the test does the computation of the concept need to be completed. This paper presents this ‘partial-closure’ canonicity test in the In-Close algorithm and compares it to a traditional CbO algorithm to demonstrate the increase in efficiency.


Formal Concept Analysis FCA FCA algorithms Computing formal concepts Canonicity test Partial-closure canonicity test Close-by-One In-Close CbO 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Conceptual Structures Research Group Communication and Computing Research Centre Faculty of Arts, Computing, Engineering and SciencesSheffield Hallam UniversitySheffieldUK

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