Computing the Duquenne–Guigues basis: an algorithm for choosing the order

Abstract

This paper presents an algorithm for choosing the order in which pseudo-intents are enumerated when computing the DuquenneGuigues basis of a formal context. Sets are constructed through the use of a spanning tree to ensure they are all found once. The time and space complexities of the algorithm are empirically evaluated using, respectively, the number of logical closures and the number of sets in memory as measures. It is found that only the space complexity depends on the enumeration order. ARTICLE HISTORY

Steps towards causal Formal Concept Analysis

“…For this reason, computing the set of pseudo-intents can be done by computing all the sets that are closed under I K (.) [1,2,25,9]. Definition 8.…”

A depth-first search algorithm for computing pseudo-closed sets

“…As such, when the algorithm reaches a new pseudo-closed set, it has already computed the closure of all its subsets that are pseudo-closed and can, thus, recognize it. Other algorithms have been proposed such as variations on NextClosure [8,18,3] based on the lectic order, the one in [4] which can enumerate in any order that extends the inclusion or the attribute-incremental algorithm in [17]. All of these share the same property: they compute all the closed sets.…”