On the shape of conceptual structures : geometry of concept lattices and n-lattices

Le stage s'effectue au laboratoire DISP, entre l'université Lyon 2 et l'INSA Lyon.

Offre complète ici : https://www.disp-lab.fr/sites/default/files/document/geometryStructuresConceptuelles.pdf

Concepts lattices are ordered structures that allow for the representation of the knowledge contained
in binary data.
When the data are multidimensional or multimodal, the
underlying structure is known as a n-lattice [2, 3].
The mathematical properties of n-lattices are not well studied,
mainly in comparison with lattices. Even their graphical
representation is an open question (a proposition exists,
shown in Fig. 2). With this internship proposal, we will work
on ordered structures like n-lattices with tools from geometry.
We propose to :
- describe the manifolds that correspond to posets
and lattices,
- describe the manifolds of n-lattices,
- study the associated metrics.
Our objective is the definition of metrics for
classification of concept lattices, and at term to define a notion of
signature for groups of structures, to align with the existing
classes of posets, and lattices.

Nous recherchons un candidat intéressé par les mathématiques appliquées à l'analyse de données. Des compétences en mathématiques discrètes ou en géométries sont les bienvenues.