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Convergence issues in Relational Concept Analysis based on AOC-posets — arXiv:2609.00054

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.00054
License (as archived): CC0-1.0
Archived: 2026-10-17T06:32:36.121Z
SHA-256 of the archived text: 0397449034182de43fde346d5ffb19b6dd436618f7f5a6ff2734a47d8361dcd9
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How to cite

Convergence issues in Relational Concept Analysis based on AOC-posets — arXiv:2609.00054 — arXiv (en), https://arxiv.org/abs/2609.00054 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_fa7c458a2ccd (Metraipolis archive dc_fa7c458a2ccd, sha256 0397449034182de43fde346d5ffb19b6dd436618f7f5a6ff2734a47d8361dcd9)

BibTeX

@misc{dcfa7c458a2ccd,
  title = {Convergence issues in Relational Concept Analysis based on AOC-posets — arXiv:2609.00054},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.00054},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_fa7c458a2ccd; sha256 0397449034182de43fde346d5ffb19b6dd436618f7f5a6ff2734a47d8361dcd9},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.00054. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Formal Concept Analysis (FCA) is an approach for conceptual classification building and rule discovery from a binary table describing a set of objects by a set of attributes. Extensions have been proposed to deal with non-binary and more complex data, such as Relational Concept Analysis (RCA) for multi-relational data. RCA aims to highlight groups of objects characterized by their relationships with other groups of objects. The richer and more complex nature of the underlying data allows RCA to produce richer results than FCA, at the expense of higher computational and interpretive complexity. The most commonly used conceptual classification structure in FCA is the concept lattice. However, in many applications, concept lattice substructures, such as AOC-posets, are preferred over the full lattice, either to mitigate combinatorial blow-up or to focus on the most informative parts of the structure. Indeed, in an AOC-poset, only concepts introducing an object or an attribute are represented, which makes AOC-posets smaller and easier to compute and use than concept lattices. Although RCA was originally defined on concept lattices, it can also be instantiated on AOC-posets. RCA is iterative and its convergence is guaranteed in the lattice-based setting, but this guarantee is lost when using AOC-posets. In this paper, we investigate this loss of convergence in detail. We show why convergence is no longer guaranteed in the general case, identify conditions under which it can still be ensured, and discuss how a dataset can be transformed to recover convergence. We also propose a convergent variant of the process, which preserves the AOC-poset structure: relational attributes, once created, are never removed, which guarantees convergence at the price of attributes that may refer to concepts absent from the final structures.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-09-02 in cs.AI).
Categorie arXiv: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2609.00054 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-17T06:15:12.718Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-09-02?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).