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Computer Science > Machine Learning

arXiv:2302.09101 (cs)
[Submitted on 17 Feb 2023]

Title:Scaling Dimension

Authors:Bernhard Ganter, Tom Hanika, Johannes Hirth
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Abstract:Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic definitions are in flux. Our contribution was triggered by the study of concept lattices for tree classifiers and the scaling methods used there. We extend some basic notions, give precise mathematical definitions for them and introduce the concept of scaling dimension. In addition to a detailed discussion of its properties, including an example, we show theoretical bounds related to the order dimension of concept lattices. We also study special subclasses, such as the ordinal and the interordinal scaling dimensions, and show for them first results and examples.
Subjects: Machine Learning (cs.LG); Artificial Intelligence (cs.AI)
MSC classes: 03G10 68T27 68T30 06B10 06A15
Cite as: arXiv:2302.09101 [cs.LG]
  (or arXiv:2302.09101v1 [cs.LG] for this version)
  https://doi.org/10.48550/arXiv.2302.09101
Related DOI: https://doi.org/10.1007/978-3-031-35949-1_5

Submission history

From: Tom Hanika [view email]
[v1] Fri, 17 Feb 2023 19:16:04 UTC (41 KB)
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