Lattices are a commonly used structure for the
representation and analysis of relational and
ontological knowledge. In particular, the analysis
of these requires a decomposition of a large and
high-dimensional lattice into a set of
understandably large parts. With the present work we
propose /ordinal motifs/ as analytical units of
meaning. We study these ordinal substructures (or
standard scales) through order-embeddings and (full)
scale-measures of formal contexts from the field of
formal concept analysis. We show that the underlying
decision problems are NP-complete and provide
results on how one can incrementally identify
ordinal motifs to save computational
effort. Accompanying our theoretical results, we
demonstrate how ordinal motifs can be leveraged to
achieve textual explanations based on principles
from human computer interaction.
Katharina B. Budde, Christian Rellstab, Myriam Heuertz, Felix Gugerli, Tom Hanika, Miguel Verdú, Juli G. Pausas, Santiago C. González-Martínez
Divergent selection in a Mediterranean pine on local
spatial scales
What is the Intrinsic Dimension of Your Binary Data? - and How to
Compute it Quickly
In: Conceptual Knowledge Structures - First International Joint Conference,
CONCEPTS 2024, Cádiz, Spain, September 9-13, 2024, Proceedings, I. Cabrera, S. Ferré, S. Obiedkov (eds.), 97–112. Springer (2024).
In: Conceptual Knowledge Structures - First International Joint Conference,
CONCEPTS 2024, Cádiz, Spain, September 9-13, 2024, Proceedings, I. Cabrera, S. Ferré, S. Obiedkov (eds.), 182–197. Springer (2024).
In: Foundations of Intelligent Systems - 24th
Int. Symposium, ISMIS 2018, M. Ceci, N. Japkowicz, J. Liu, G. Papadopoulos, Z. Ras (eds.), 56-66. Springer (2018).
Martin Atzmueller, Tom Hanika, Gerd Stumme, Richard Schaller, Bernd Ludwig
Social event network analysis: Structure,
preferences, and reality
In: 2016 IEEE/ACM Int. Conf. on Advances in Social
Networks Analysis and Mining, R. Kumar, J. Caverlee, H. Tong (eds.), 613–620. IEEE Computer Society (2016).