A New Algorithm based on Extent Bit-array for Computing Formal Concepts. (arXiv:2111.00003v1 [cs.AI])

The emergence of Formal Concept Analysis (FCA) as a data analysis technique
has increased the need for developing algorithms which can compute formal
concepts quickly. The current efficient algorithms for FCA are variants of the
Close-By-One (CbO) algorithm, such as In-Close2, In-Close3 and In-Close4, which
are all based on horizontal storage of contexts. In this paper, based on
algorithm In-Close4, a new algorithm based on the vertical storage of contexts,
called In-Close5, is proposed, which can significantly reduce both the time
complexity and space complexity of algorithm In-Close4. Technically, the new
algorithm stores both context and extent of a concept as a vertical bit-array,
while within In-Close4 algorithm the context is stored only as a horizontal
bit-array, which is very slow in finding the intersection of two extent sets.
Experimental results demonstrate that the proposed algorithm is much more
effective than In-Close4 algorithm, and it also has a broader scope of
applicability in computing formal concept in which one can solve the problems
that cannot be solved by the In-Close4 algorithm.

Source: https://arxiv.org/abs/2111.00003

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