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Fast algorithms for implication bases and attribute exploration using proper premises

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Abstract

A central task in formal concept analysis is the enumeration of a small base for the implications that hold in a formal context. The usual stem base algorithms have been proven to be costly in terms of runtime. Proper premises are an alternative to the stem base. We present a new algorithm for the fast computation of proper premises. It is based on a known link between proper premises and minimal hypergraph transversals. Two further improvements are made, which reduce the number of proper premises that are obtained multiple times and redundancies within the set of proper premises. We have evaluated our algorithms within an application related to refactoring of model variants. In this application an implicational base needs to be computed, and runtime is more crucial than minimal cardinality. In addition to the empirical tests, we provide heuristic evidence that an approach based on proper premises will also be beneficial for other applications. Finally, we show how our algorithms can be extended to an exploration algorithm that is based on proper premises.

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Authors and Affiliations

  1. Institute of Applied Computer Science, Technische Universität Dresden, Dresden, Germany

    Uwe Ryssel

  2. Institute of Theoretical Computer Science, Technische Universität Dresden, Dresden, Germany

    Felix Distel & Daniel Borchmann

Authors
  1. Uwe Ryssel
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  2. Felix Distel
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  3. Daniel Borchmann
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Corresponding author

Correspondence to Felix Distel.

Additional information

The author Daniel Borchmann has been supported by DFG Graduiertenkolleg 1763 (QuantLA).

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Ryssel, U., Distel, F. & Borchmann, D. Fast algorithms for implication bases and attribute exploration using proper premises. Ann Math Artif Intell 70, 25–53 (2014). https://doi.org/10.1007/s10472-013-9355-9

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  • DOI: https://doi.org/10.1007/s10472-013-9355-9

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