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articles by Karell Bertet

Research paper thumbnail of Treillis dichotomiques et arbres de décision.

Research paper thumbnail of Dichotomic lattices and local discretization for Galois lattices

Papers by Karell Bertet

Research paper thumbnail of Enrichment and visualization of visitor trajectories in a museum

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of Temporal Sequence Mining Using FCA and GALACTIC

Lecture Notes in Computer Science, 2021

Research paper thumbnail of Weak-order extensions of an order

Springer eBooks, 1997

In this paper, at ÿrst we describe a digraph representing all the weak-order extensions of a part... more In this paper, at ÿrst we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.

Research paper thumbnail of Computer Vision Applied to Comic Book Images

HAL (Le Centre pour la Communication Scientifique Directe), Feb 7, 2017

Research paper thumbnail of Discover spatio-temporal cluster from trajectory data enhance by heterogeneous contextual knowledge using FCA and the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ Algorithm

HAL (Le Centre pour la Communication Scientifique Directe), Jun 20, 2022

Research paper thumbnail of On the links between the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ algorithm and generalized convex hulls

HAL (Le Centre pour la Communication Scientifique Directe), Apr 6, 2022

Research paper thumbnail of GALACTIC: GAlois LAttices, Concept Theory, Implicational systems and Closures. A set of python3 packages for studying Formal Concept Analysis

HAL (Le Centre pour la Communication Scientifique Directe), Dec 1, 2020

Research paper thumbnail of On the links between NextPriorityConcept algorithm and generalized convex hulls

HAL (Le Centre pour la Communication Scientifique Directe), Apr 6, 2022

Research paper thumbnail of Fouille de séquences temporelles avec l’AFC et l’outil GALACTIC

HAL (Le Centre pour la Communication Scientifique Directe), Jan 24, 2022

Research paper thumbnail of Vers une réduction du fossé sémantique dans le traitement des images de documents anciens à base d’ontologies : Application aux lettrines

HAL (Le Centre pour la Communication Scientifique Directe), 2014

Nous presentons dans cet article une approche de reduction du fosse semantique dans le traitement... more Nous presentons dans cet article une approche de reduction du fosse semantique dans le traitement des documents anciens, et plus particulierement les images de lettrines. Cette approche modelise les connaissances de deux domaines (experts historiens et experts en traitement d’images) au sein d’ontologies. Cette demarche permet d’etablir des liens entre ces domaines afin d’aider les historiens a interpreter ces images et a les situer dans le temps. Nous avons combine trois ontologies (thesaurus defini par les historiens, ontologie du traitement d’image et ontologie spatiale) pour l’annotation de ces images; ainsi nous avons donc defini des regles permettant d’annoter certaines regions de l’image comme etant la lettre, une partie du corps de personnage ou encore de caracteriser une lettrine comme figurative. Des experimentations prouvent la pertinence du systeme dans l’annotation automatique d’images. Par ailleurs, la genericite de l’approche permet d’en envisager une exploitation dans d’autres contextes combinant analyse d’image, analyse spatiale et semantique du domaine, comme par exemple des images de bandes dessinees Tsopze et al. (2012).

Research paper thumbnail of An Overview of Λ-Type Operations on Quasi-Symmetric Functions

Communications in Algebra, Jul 31, 2001

We present an overview of Λ-type operations on the algebra of quasi-symmetric functions. Nous pré... more We present an overview of Λ-type operations on the algebra of quasi-symmetric functions. Nous présentons un survol de l'ensemble des propriétés de type Λ-anneau de l'algèbre des fonctions quasi-symétriques.

Research paper thumbnail of On the Joint Use of a Structural Signature and a Galois Lattice Classifier for Symbol Recognition

Springer eBooks, Sep 20, 2008

In this paper, we propose a new approach for symbol recognition using structural signatures and a... more In this paper, we propose a new approach for symbol recognition using structural signatures and a Galois Lattice as classifier. The structural signatures are based on topological graphs computed from segments which are extracted from the symbol images by using an adapted Hough transform. These structural signatures, which can be seen as dynamic paths which carry high level information, are robust towards various transformations. They are classified by using a Galois Lattice as a classifier. The performances of the proposed approach are evaluated on the GREC03 symbol database and the experimental results we obtain are encouraging.

Research paper thumbnail of A New Adaptive Structural Signature for Symbol Recognition by Using a Galois Lattice as a Classifier

IEEE transactions on systems, man, and cybernetics, Aug 1, 2011

In this paper, we propose a new approach for symbol recognition using structural signatures and a... more In this paper, we propose a new approach for symbol recognition using structural signatures and a Galois lattice as a classifier. The structural signatures are based on topological graphs computed from segments which are extracted from the symbol images by using an adapted Hough transform. These structural signatures-that can be seen as dynamic paths which carry high-level information-are robust toward various transformations. They are classified by using a Galois lattice as a classifier. The performance of the proposed approach is evaluated based on the GREC'03 symbol database, and the experimental results we obtain are encouraging.

Research paper thumbnail of Interval-based sequence mining using FCA and the NextPriorityConcept algorithm

HAL (Le Centre pour la Communication Scientifique Directe), Aug 29, 2020

Research paper thumbnail of A fuzzy precedence graph definition for algebra-based dimension reduction

The ability to obtain a compact description of an object and to keep the significant information ... more The ability to obtain a compact description of an object and to keep the significant information can be crucial for many applications such as indexing, clustering and classification. Formal concept analysis (FCA) provides an algorithm to perform such dimension reduction. However, the requirements of FCA limit its performance. In order to relax FCA requirements, this paper presents an extension of FCA with the definition and formal analysis of a fuzzy precedence graph. This is completed by a fuzzy dimension reduction algorithm. We have tested our algorithm on several real datasets related to bag of visual words and evaluated it for a classification task. The proposed formalism and algorithm improve FCA tools on several cases while retaining the significant information. Furthermore, the fuzzy dimension reduction algorithm never performs worse than FCA tools in terms of dimension reduction. We have also compared it with PCA dimension reduction. PCA usually reduces more attributes but looses more information and does so in an unreliable/unstable manner compared to our algorithm.

Research paper thumbnail of Preface: Concept Lattices and Applications: Recent Advances and New Opportunities

Discrete Applied Mathematics

Formal Concept Analysis is a mathematical theory formalizing aspects of human conceptual thinking... more Formal Concept Analysis is a mathematical theory formalizing aspects of human conceptual thinking by means of lattice theory. As such, it constitutes a theoretically well-founded, practically proven, human-centered approach to data science and has been continuously contributing valuable insights, methodologies, and algorithms to the scientific community. The International Conference Concept Lattices and Their Applications (CLA) has been organized since 2002 with the aim of providing a forum for researchers involved in all aspects of the study of FCA, from theory to implementations and practical applications. Previous years' conferences took place

Research paper thumbnail of Analysis of Complex and Heterogeneous Data Using FCA and Monadic Predicates

Springer eBooks, Apr 1, 2022

Research paper thumbnail of Problématique de la recommandation sans évaluation

HAL (Le Centre pour la Communication Scientifique Directe), May 26, 2015

Research paper thumbnail of Treillis dichotomiques et arbres de décision.

Research paper thumbnail of Dichotomic lattices and local discretization for Galois lattices

Research paper thumbnail of Enrichment and visualization of visitor trajectories in a museum

HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific re... more HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L'archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

Research paper thumbnail of Temporal Sequence Mining Using FCA and GALACTIC

Lecture Notes in Computer Science, 2021

Research paper thumbnail of Weak-order extensions of an order

Springer eBooks, 1997

In this paper, at ÿrst we describe a digraph representing all the weak-order extensions of a part... more In this paper, at ÿrst we describe a digraph representing all the weak-order extensions of a partially ordered set and algorithms for generating them. Then we present a digraph representing all of the minimal weak-order extensions of a partially ordered set. This digraph also implies generation algorithms. Finally, we prove that the number of weak-order extensions of a partially ordered set is a comparability invariant, whereas the number of minimal weak-order extensions of a partially ordered set is not a comparability invariant.

Research paper thumbnail of Computer Vision Applied to Comic Book Images

HAL (Le Centre pour la Communication Scientifique Directe), Feb 7, 2017

Research paper thumbnail of Discover spatio-temporal cluster from trajectory data enhance by heterogeneous contextual knowledge using FCA and the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ Algorithm

HAL (Le Centre pour la Communication Scientifique Directe), Jun 20, 2022

Research paper thumbnail of On the links between the NᴇxᴛPʀɪᴏʀɪᴛʏCᴏɴᴄᴇᴘᴛ algorithm and generalized convex hulls

HAL (Le Centre pour la Communication Scientifique Directe), Apr 6, 2022

Research paper thumbnail of GALACTIC: GAlois LAttices, Concept Theory, Implicational systems and Closures. A set of python3 packages for studying Formal Concept Analysis

HAL (Le Centre pour la Communication Scientifique Directe), Dec 1, 2020

Research paper thumbnail of On the links between NextPriorityConcept algorithm and generalized convex hulls

HAL (Le Centre pour la Communication Scientifique Directe), Apr 6, 2022

Research paper thumbnail of Fouille de séquences temporelles avec l’AFC et l’outil GALACTIC

HAL (Le Centre pour la Communication Scientifique Directe), Jan 24, 2022

Research paper thumbnail of Vers une réduction du fossé sémantique dans le traitement des images de documents anciens à base d’ontologies : Application aux lettrines

HAL (Le Centre pour la Communication Scientifique Directe), 2014

Nous presentons dans cet article une approche de reduction du fosse semantique dans le traitement... more Nous presentons dans cet article une approche de reduction du fosse semantique dans le traitement des documents anciens, et plus particulierement les images de lettrines. Cette approche modelise les connaissances de deux domaines (experts historiens et experts en traitement d’images) au sein d’ontologies. Cette demarche permet d’etablir des liens entre ces domaines afin d’aider les historiens a interpreter ces images et a les situer dans le temps. Nous avons combine trois ontologies (thesaurus defini par les historiens, ontologie du traitement d’image et ontologie spatiale) pour l’annotation de ces images; ainsi nous avons donc defini des regles permettant d’annoter certaines regions de l’image comme etant la lettre, une partie du corps de personnage ou encore de caracteriser une lettrine comme figurative. Des experimentations prouvent la pertinence du systeme dans l’annotation automatique d’images. Par ailleurs, la genericite de l’approche permet d’en envisager une exploitation dans d’autres contextes combinant analyse d’image, analyse spatiale et semantique du domaine, comme par exemple des images de bandes dessinees Tsopze et al. (2012).

Research paper thumbnail of An Overview of Λ-Type Operations on Quasi-Symmetric Functions

Communications in Algebra, Jul 31, 2001

We present an overview of Λ-type operations on the algebra of quasi-symmetric functions. Nous pré... more We present an overview of Λ-type operations on the algebra of quasi-symmetric functions. Nous présentons un survol de l'ensemble des propriétés de type Λ-anneau de l'algèbre des fonctions quasi-symétriques.

Research paper thumbnail of On the Joint Use of a Structural Signature and a Galois Lattice Classifier for Symbol Recognition

Springer eBooks, Sep 20, 2008

In this paper, we propose a new approach for symbol recognition using structural signatures and a... more In this paper, we propose a new approach for symbol recognition using structural signatures and a Galois Lattice as classifier. The structural signatures are based on topological graphs computed from segments which are extracted from the symbol images by using an adapted Hough transform. These structural signatures, which can be seen as dynamic paths which carry high level information, are robust towards various transformations. They are classified by using a Galois Lattice as a classifier. The performances of the proposed approach are evaluated on the GREC03 symbol database and the experimental results we obtain are encouraging.

Research paper thumbnail of A New Adaptive Structural Signature for Symbol Recognition by Using a Galois Lattice as a Classifier

IEEE transactions on systems, man, and cybernetics, Aug 1, 2011

In this paper, we propose a new approach for symbol recognition using structural signatures and a... more In this paper, we propose a new approach for symbol recognition using structural signatures and a Galois lattice as a classifier. The structural signatures are based on topological graphs computed from segments which are extracted from the symbol images by using an adapted Hough transform. These structural signatures-that can be seen as dynamic paths which carry high-level information-are robust toward various transformations. They are classified by using a Galois lattice as a classifier. The performance of the proposed approach is evaluated based on the GREC'03 symbol database, and the experimental results we obtain are encouraging.

Research paper thumbnail of Interval-based sequence mining using FCA and the NextPriorityConcept algorithm

HAL (Le Centre pour la Communication Scientifique Directe), Aug 29, 2020

Research paper thumbnail of A fuzzy precedence graph definition for algebra-based dimension reduction

The ability to obtain a compact description of an object and to keep the significant information ... more The ability to obtain a compact description of an object and to keep the significant information can be crucial for many applications such as indexing, clustering and classification. Formal concept analysis (FCA) provides an algorithm to perform such dimension reduction. However, the requirements of FCA limit its performance. In order to relax FCA requirements, this paper presents an extension of FCA with the definition and formal analysis of a fuzzy precedence graph. This is completed by a fuzzy dimension reduction algorithm. We have tested our algorithm on several real datasets related to bag of visual words and evaluated it for a classification task. The proposed formalism and algorithm improve FCA tools on several cases while retaining the significant information. Furthermore, the fuzzy dimension reduction algorithm never performs worse than FCA tools in terms of dimension reduction. We have also compared it with PCA dimension reduction. PCA usually reduces more attributes but looses more information and does so in an unreliable/unstable manner compared to our algorithm.

Research paper thumbnail of Preface: Concept Lattices and Applications: Recent Advances and New Opportunities

Discrete Applied Mathematics

Formal Concept Analysis is a mathematical theory formalizing aspects of human conceptual thinking... more Formal Concept Analysis is a mathematical theory formalizing aspects of human conceptual thinking by means of lattice theory. As such, it constitutes a theoretically well-founded, practically proven, human-centered approach to data science and has been continuously contributing valuable insights, methodologies, and algorithms to the scientific community. The International Conference Concept Lattices and Their Applications (CLA) has been organized since 2002 with the aim of providing a forum for researchers involved in all aspects of the study of FCA, from theory to implementations and practical applications. Previous years' conferences took place

Research paper thumbnail of Analysis of Complex and Heterogeneous Data Using FCA and Monadic Predicates

Springer eBooks, Apr 1, 2022

Research paper thumbnail of Problématique de la recommandation sans évaluation

HAL (Le Centre pour la Communication Scientifique Directe), May 26, 2015

Research paper thumbnail of GALACTIC: a python framework for Formal Concept Analysis

HAL (Le Centre pour la Communication Scientifique Directe), Jul 1, 2021

Research paper thumbnail of A Story of Rules

International Conference on Formal Concept Analysis, Jun 29, 2021

Research paper thumbnail of A local discretization of continuous data for lattices: Technical aspects

The Eighth International Conference on Concept Lattices and Their Applications, 2011

Research paper thumbnail of Some Links Between Decision Tree and Dichotomic Lattice

Proceedings of the Sixth International Conference on Concept Lattices and Their Applications, 2008

There are two types of classification methods using a Galois lattice: as most of them rely on sel... more There are two types of classification methods using a Galois lattice: as most of them rely on selection, recent research work focus on navigationbased approaches. In navigation-oriented methods, classification is performed by navigating through the complete lattice, similar to the decision tree. When defined from binary attributes obtained after a discretization pre-processing step, and more generally when a non-empty set of complementarity attributes can be associated to each binary attribute, lattices are denoted as "dichotomic lattices". The Navigala approach is a navigation-based classification method that relies on the use of a dichotomic lattice. It was initially proposed for symbol recognition in the field of technical document image analysis. In this paper, we define the structural links between decision trees and dichotomic lattices defined from the same table of data described by binary attributes. Under this condition, we prove both that every decision tree is included in the dichotomic lattice and that the dichotomic lattice is the merger of all the decision trees that can be constructed from the same binary data table.