A New Algorithm based on Extent Bit-array for Computing Formal Concepts

TL;DR

This paper introduces In-Close5, a novel algorithm for Formal Concept Analysis that uses vertical bit-array storage to improve speed and efficiency over previous horizontal storage methods, enabling faster and broader formal concept computation.

Contribution

It presents a new vertical storage-based algorithm, In-Close5, improving on In-Close4 by reducing time and space complexity for formal concept computation.

Findings

In-Close5 outperforms In-Close4 in speed and efficiency.

The algorithm can solve problems previously unsolvable by In-Close4.

Experimental results confirm significant performance improvements.

Abstract

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.