9 research outputs found
From-Below Boolean Matrix Factorization Algorithm Based on MDL
During the past few years Boolean matrix factorization (BMF) has become an
important direction in data analysis. The minimum description length principle
(MDL) was successfully adapted in BMF for the model order selection.
Nevertheless, a BMF algorithm performing good results from the standpoint of
standard measures in BMF is missing. In this paper, we propose a novel
from-below Boolean matrix factorization algorithm based on formal concept
analysis. The algorithm utilizes the MDL principle as a criterion for the
factor selection. On various experiments we show that the proposed algorithm
outperforms---from different standpoints---existing state-of-the-art BMF
algorithms
Analyse de Concepts Formels, distributivité et modèles de graphes médians pour la phylogénie
National audienceLa phylogénie est l’étude des relations de parentés entre les êtres vivants. La classification phylogénétique consiste à classer les êtres vivants à partir de données de phylogénie. Traditionnellement, les modèles utilisés pour ce faire sont les arbres phylogénétiques. Ces arbres ne permettent cependant pas de capturer toute la complexité des phénomènes évolutifs. Du fait de cette complexité, plusieurs arbres peuvent convenir. Pour ne pas privilégier de solution particulière, l’utilisation de graphes médians permet d’encoder l’ensemble des arbres dans un graphe particulier, le graphe médian. Les graphes médians ont des liens étroits avec certains types de treillis, une autre structure souvent utilisée en classification. L’Analyse de Concepts Formels (FCA) a fait des treillis de concepts l’objet central d’étude pour des problèmes d’analyse de données. Dans cet article, nous montrons comment utiliser la FCA pour produire des graphes médians, et nous mettons en avant les verrous techniques à franchir
Towards Distributivity in FCA for Phylogenetic Data
International audienceIt is known that a distributive lattice is a median graph, and that a distributive ∨-semilattice can be thought of as a median graph iff every triple of elements such that the infimum of each couple of its elements exists, has an infimum. Since a lattice without its bottom element is obviously a ∨-semilattice, using the FCA formalism, we investigate the following problem: Given a semilattice L obtained from a lattice by deletion of the bottom element, is there a minimum distributive ∨-semilattice L d such that L can be order embedded into L d ? We give a negative answer to this question by providing a counterexample
Embedding median graphs into minimal distributive ∨-semi-lattices
International audienceIt is known that a distributive lattice is a median graph, and that a distributive ∨-semi-lattice can be thought of as a median graph i every triple of elements such that the inmum of each couple of its elements exists, has an inmum. Since a lattice without its bottom element is obviously a ∨-semi-lattice, using the FCA formalism, we investigate the following problem: Given a semi-lattice L obtained from a lattice by deletion of the bottom element, is there a minimum distributive ∨-semi-lattice L d such that L can be order embedded into L d ? We give a negative answer to this question by providing a counter example
Efficient Axiomatization of OWL 2 EL Ontologies from Data by means of Formal Concept Analysis: (Extended Version)
We present an FCA-based axiomatization method that produces a complete EL TBox (the terminological part of an OWL 2 EL ontology) from a graph dataset in at most
exponential time. We describe technical details that allow for efficient implementation as well as variations that dispense with the computation of extremely large axioms, thereby
rendering the approach applicable albeit some completeness is lost. Moreover, we evaluate the prototype on real-world datasets.This is an extended version of an article accepted at AAAI 2024
Eighth International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI at ECAI 2020)
International audienceProceedings of the 8th International Workshop "What can FCA do for Artificial Intelligence?" (FCA4AI 2020)co-located with 24th European Conference on Artificial Intelligence (ECAI 2020), Santiago de Compostela, Spain, August 29, 202
The distributive, graded lattice of EL concept descriptions and its neighborhood relation: Extended Version
For the description logic EL, we consider the neighborhood relation which is induced by the subsumption order, and we show that the corresponding lattice of EL concept descriptions is distributive, modular, graded, and metric. In particular, this implies the existence of a rank function as well as the existence of a distance function
Société Francophone de Classification (SFC) Actes des 26èmes Rencontres
National audienceLes actes des rencontres de la Société Francophone de Classification (SFC, http://www.sfc-classification.net/) contiennent l'ensemble des contributions,présentés lors des rencontres entre les 3 et 5 septembre 2019 au Centre de Recherche Inria Nancy Grand Est/LORIA Nancy. La classification sous toutes ces formes, mathématiques, informatique (apprentissage, fouille de données et découverte de connaissances ...), et statistiques, est la thématique étudiée lors de ces journées. L'idée est d'illustrer les différentes facettes de la classification qui reflètent les intérêts des chercheurs dans la matière, provenant des mathématiques et de l'informatique