Abstract
Formal Concept Analysis (FCA) transforms a context bigraph, having vertices of type object and attribute, into a lattice digraph, whose vertices and arcs represent formal concepts and their covering relation. The computational complexity of most FCA algorithms is a polynomial function of the numbers of vertices in both the context bigraph and lattice digraph. While the latter quantity is fixed, the former can be decreased by context standardisation, a process which we show is facilitated by the efficient partition refinement algorithm of Spinrad.
The Carve algorithm recursively partitions the context bigraph and corresponding lattice digraph by removing universal objects and attributes and their orphans and partitioning the resultant sub-context into its connected components. The associated software prototype uses the resultant tree structure to support coordinated browsing of both. This paper describes an additional, coordinated representation of the context bigraph which makes explicit in its bi-adjacency matrix the pattern of nested sub-contexts discovered by the Carve algorithm. We show that permuting this matrix into doubly-lexical order with the aid of Spinrad’s algorithm groups together into nested rectangles the bigraph edges belonging to these sub-contexts, and facilitates the two key processing steps of the Carve algorithm.
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Notes
- 1.
The truth of a sentence containing terms in square brackets is unchanged by substituting these terms for those which precede them.
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Pattison, T., Nataraja, A. (2023). Doubly-Lexical Order Supports Standardisation and Recursive Partitioning of Formal Context. In: Dürrschnabel, D., López Rodríguez, D. (eds) Formal Concept Analysis. ICFCA 2023. Lecture Notes in Computer Science(), vol 13934. Springer, Cham. https://doi.org/10.1007/978-3-031-35949-1_2
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