Convergence issues in Relational Concept Analysis based on AOC-posets
Mirrored from arXiv — Machine Learning for archival readability. Support the source by reading on the original site.
Computer Science > Machine Learning
arXiv:2609.00054 (cs)
[Submitted on 30 Aug 2026]
Title:Convergence issues in Relational Concept Analysis based on AOC-posets
View a PDF of the paper titled Convergence issues in Relational Concept Analysis based on AOC-posets, by Xavier Dolques and 4 other authors
View PDF
HTML (experimental)
Abstract: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.
| Subjects: | Machine Learning (cs.LG) |
| Cite as: | arXiv:2609.00054 [cs.LG] |
| (or arXiv:2609.00054v1 [cs.LG] for this version) | |
| https://doi.org/10.48550/arXiv.2609.00054
arXiv-issued DOI via DataCite
|
Submission history
From: Marianne Huchard Mrs [view email][v1] Sun, 30 Aug 2026 10:09:37 UTC (1,177 KB)
Full-text links:
Access Paper:
- View PDF
- HTML (experimental)
- TeX Source
View a PDF of the paper titled Convergence issues in Relational Concept Analysis based on AOC-posets, by Xavier Dolques and 4 other authors
References & Citations
Loading...
Bookmark
Bibliographic Tools
Code, Data, Media
Demos
Related Papers
About arXivLabs
Bibliographic and Citation Tools
Bibliographic Explorer Toggle
Bibliographic Explorer (What is the Explorer?)
Connected Papers Toggle
Connected Papers (What is Connected Papers?)
Litmaps Toggle
Litmaps (What is Litmaps?)
scite.ai Toggle
scite Smart Citations (What are Smart Citations?)
Code, Data and Media Associated with this Article
alphaXiv Toggle
alphaXiv (What is alphaXiv?)
Links to Code Toggle
CatalyzeX Code Finder for Papers (What is CatalyzeX?)
DagsHub Toggle
DagsHub (What is DagsHub?)
GotitPub Toggle
Gotit.pub (What is GotitPub?)
Huggingface Toggle
Hugging Face (What is Huggingface?)
ScienceCast Toggle
ScienceCast (What is ScienceCast?)
Demos
Replicate Toggle
Replicate (What is Replicate?)
Spaces Toggle
Hugging Face Spaces (What is Spaces?)
Spaces Toggle
TXYZ.AI (What is TXYZ.AI?)
Recommenders and Search Tools
Link to Influence Flower
Influence Flower (What are Influence Flowers?)
Core recommender toggle
CORE Recommender (What is CORE?)
IArxiv recommender toggle
IArxiv Recommender
(What is IArxiv?)
arXivLabs: experimental projects with community collaborators
arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.
Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.
Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.
More from arXiv — Machine Learning
-
Algebraic Integer Quantization for Machine Learning Applications
Oct 12
-
CircuitTree: Composing Circuits into A Syllable Transcriber
Oct 12
-
Behind-the-Meter Photovoltaic Visibility from Net Smart Meters: Deployment Regimes and Operational Insights
Oct 12
-
GlucoPRISM: Protocol-Supervised Pretraining for Cross-Cohort Glucose Transfer
Oct 12
Discussion (0)
Sign in to join the discussion. Free account, 30 seconds — email code or GitHub.
Sign in →No comments yet. Sign in and be the first to say something.