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

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

Steps Towards Achieving Distributivity in Formal Concept Analysis

International audienceIn this paper we study distributive lattices in the framework of Formal Concept Analysis (FCA). The main motivation comes from phylogeny where biological derivations and parsimonious trees can be represented as median graphs. There exists a close connection between distributive lattices and median graphs. Moreover, FCA provides efficient algorithms to build concept lattices. However, a concept lattice is not necessarily distributive and thus it is not necessarily a median graph.In this paper we investigate possible ways of transforming a concept lattice into a distributive one, by making use Birkhoff’s representation of distributive lattices. We detail the operation that transforms a reduced context into a context of a distributive lattice. This allows us to reuse the FCA algorithmic machinery to build and to visualize distributive concept lattices, and then to study the associated median graphs

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

Contribution à l'étude de la distributivité d'un treillis de concepts

National audienceNous nous intéressons aux treillis distributifs dans le cadre de l'analyse formelle de concepts (FCA). La motivation primitive vient de la phylogénie et des graphes médians pour représenter les dérivations biologiques et les arbres parcimonieux. La FCA propose des algorithmes efficaces de construction de treillis de concepts. Cependant, un treillis de concepts n'est pas en correspondance avec un graphe médian sauf s'il est distributif, d'où l'idée d'étudier la transformation d'un treillis de concepts en un treillis distributif. Pour ce faire, nous nous appuyons sur le théorème de représentation de Birkhoff qui nous permet de systématiser la transformation d'un contexte quelconque en un contexte de treillis de concepts distributif. Ainsi, nous pouvons bénéficier de l'algorithmique de FCA pour construire mais aussi visualiser les treillis de concepts distributifs, et enfin étudier les graphes médians associés

Steps in the Representation of Concept Lattices and Median Graphs

International audienceMedian semilattices have been shown to be useful for dealing with phylogenetic classication problems since they subsume median graphs, distributive lattices as well as other tree based classica-tion structures. Median semilattices can be thought of as distributive ∨-semilattices that satisfy the following property (TRI): for every triple x, y, z, if x ∧ y, y ∧ z and x ∧ z exist, then x ∧ y ∧ z also exists. In previous work we provided an algorithm to embed a concept lattice L into a dis-tributive ∨-semilattice, regardless of (TRI). In this paper, we take (TRI) into account and we show that it is an invariant of our algorithmic approach. This leads to an extension of the original algorithm that runs in polynomial time while ensuring that the output is a median semilattice

K-spectral centroid : extension et optimisations

International audienceIn this work, we address the problem of unsupervised classification of large time series datasets. We focus on K-Spectral Centroid (KSC), a k-means-like model, devised for time series clustering. KSC relies on a custom dissimilarity measure between time series, which is invariant to time shifting and Y-scaling. KSC has two downsides: firstly its dissimilarity measure only makes sense for non negative time series. Secondly the KSC algorithm is relatively demanding in terms of computation time. In this paper, we present a natural extension of the KSC dissimilarity measure to time series of arbitrary signs. We show that this new measure is a metric distance. We propose to speed up this extended KSC (EKSC) thanks to four exact optimizations. Finally, we compare EKSC to a similar model, K-Shape, on real world datasets

Comparaison et Partitionnement de Séries Temporelles Basés sur la Forme des Séries

International audienceIn this work, we propose two k-means-like methods, devised for time series clustering.Each method relies on a custom dissimilarity measure between time series, which is invariant to time shifting and Y-scaling.The first measure is an adaptation of the cosine dissimilarity for which the best time alignment is obtained by testing all temporal translations.The second measure is a soft version of the first measure: the min computation on the different time alignmentsis carried out by the soft min function.Dans ce travail, nous nous intéressons à la classification non super-visée de séries temporelles. La méthode de partitionnement utilisée, dérivée des centres mobiles, s'appuie sur la forme des séries pour évaluer leurs ressemblances. Afin de comparer ces formes, nous proposons deux mesures de ressemblance entre séries temporelles invariantes par translation et par changement d'échelle. La première mesure est une adaptation de la mesure cosine pour laquelle l'alignement temporel optimal entre deux séries est obtenu en testant toutes les translations d'une série par rapport à l'autre. La seconde mesure est une version soft de la première : le calcul du min sur les différents alignements est effectué grâce à la fonction softmin

Monalysin, a Novel ß-Pore-Forming Toxin from the Drosophila Pathogen Pseudomonas entomophila, Contributes to Host Intestinal Damage and Lethality

Pseudomonas entomophila is an entomopathogenic bacterium that infects and kills Drosophila. P. entomophila pathogenicity is linked to its ability to cause irreversible damages to the Drosophila gut, preventing epithelium renewal and repair. Here we report the identification of a novel pore-forming toxin (PFT), Monalysin, which contributes to the virulence of P. entomophila against Drosophila. Our data show that Monalysin requires N-terminal cleavage to become fully active, forms oligomers in vitro, and induces pore-formation in artificial lipid membranes. The prediction of the secondary structure of the membrane-spanning domain indicates that Monalysin is a PFT of the ß-type. The expression of Monalysin is regulated by both the GacS/GacA two-component system and the Pvf regulator, two signaling systems that control P. entomophila pathogenicity. In addition, AprA, a metallo-protease secreted by P. entomophila, can induce the rapid cleavage of pro-Monalysin into its active form. Reduced cell death is observed upon infection with a mutant deficient in Monalysin production showing that Monalysin plays a role in P. entomophila ability to induce intestinal cell damages, which is consistent with its activity as a PFT. Our study together with the well-established action of Bacillus thuringiensis Cry toxins suggests that production of PFTs is a common strategy of entomopathogens to disrupt insect gut homeostasis