A Análise de Conceitos Formais (FCA) é uma teoria matemática que formaliza a noção de conceitos e hierarquias conceituais. De importância central a esta teoria é uma estrutura algébrica denominada reticulado de conceitos. Esta estrutura é definida em função de um conjunto de objetos, outro de atributos e uma relação que indica os atributos apresentados por cada objeto. Uma representação gráfica de um reticulado de conceitos, por meio de uma interface computacional, é capaz de expor regularidades presentes em dados a um usuário, e este pode então realizar tarefas de análise exploratória de dados. Este tipo de aplicação de FCA vem sendo empregado em dezenas de projetos pertencentes a áreas diversas, como medicina, serviços de inteligência, engenharia de software e bioinformática. Mostramos neste trabalho um sistema de análise exploratória de dados baseado em FCA, e sua utilização sobre dados reais. Também é mostrado como reticulados de conceitos podem ser empregados em interfaces de recuperação de informação. Do ponto de vista algorítmico, analisamos métodos computacionais para a determinação do reticulado de conceitos, e também de uma subestrutura simplificada, o conjunto de conceitos. O tamanho de um reticulado de conceitos pode ser exponencial em função dos tamanhos dos conjuntos de objetos e de atributos. Assim, é de vital interesse o estabelecimento de cotas superiores para o número de conceitos de um reticulado. Neste trabalho, apresentamos as cotas já conhecidas presentes na literatura. Também estabelecemos uma nova cota superior, e mostramos famílias de casos em que nossa cota superior é mais justa que as demais. Para algumas famílias particulares, nossa cota é polinomial, enquanto que as demais são exponenciais. / Formal Concept Analysis (FCA) is a mathematical theory that formalizes the notion of concepts and conceptual hierarchies. Of central importance to this theory is an algebraic structure termed concept lattice. Such structure becomes defined after being given one set of objects, one of attributes, and an incidence relation describing the attributes held by each object. A graphical representation of a concept lattice, by means of a computational interface, is capable of unfolding regularities present in data to an user, who is then able to conduct exploratory data analysis tasks. This sort of FCA application is currently deployed in tens of projects belonging to a wide range of areas, such as medicine, intelligence services, software engineering and bioinformatics. We show in this work an FCA-based system of exploratory data analysis, and its use over real data. Moreover, it is shown how concept lattices can be employed in information retrieval interfaces. From the algorithmic viewpoint, we analyse computational methods for the determination of a concept lattice, and also of a simplified substructure, the concept set. The size of a concept lattice can be exponential when compared to the size of the objects and the attributes sets. Therefore, it is of paramount interest the establishment of upper bounds for the number of concepts of a lattice. In this work, we present the upper bounds already known in the literature. We also establish a new upper bound, and show families of cases in which our bound is sharper than the others. For particular families, our bound is polynomial, whereas the other bounds are exponential.

Des familles de logiciels similaires proviennent fréquemment de pratiques de réutilisation de clones de logiciels existants, qui sont ensuite enrichis ou dépouillés de fonctionnalités pour suivre de nouvelles exigences. Avec le temps, ces variantes se multiplient et se complexifient, et il devient difficile de les maintenir, de les faire évoluer. L’ingénierie des lignes de produits logiciels regroupe un ensemble de méthodes visant à faciliter le développement et la gestion de telles collections de logiciels similaires. Documenter la variabilité est le point central de ce paradigme ; on la représente à travers des modèles de variabilité, qui servent de supports à la grande majorité des processus propres à l’ingénierie des lignes de produits. La migration complète ou partielle de ces familles de logiciels vers des approches de type lignes de produits permet la simplification de leur exploitation. La rétro-ingénierie, la modélisation et la gestion de la variabilité sont reconnues comme une phase cruciale et ardue de cette migration. Par conséquent, de nombreuses approches ont été proposées pour étudier des descriptions de familles de logiciels dans ce but. Plusieurs d’entre elles s’appuient sur l’analyse formelle de concepts, un cadre mathématique de groupement hiérarchique qui organise un ensemble d’objets et leurs descriptions dans une structure canonique mettant naturellement en évidence leurs aspects communs et variables.Dans ce manuscrit, nous défendons l'idée que l’analyse formelle de concepts, plus qu’un outil, offre un véritable cadre structurel et réutilisable à l’étude de la variabilité des familles de produits.Dans un premier temps, nous établissons un panorama des informations sur la variabilité qui sont mises en évidence grâce à ce formalisme, et discutons de son spectre d’applicabilité. Nous étudions les points communs entre les structures conceptuelles produites par l’analyse formelle de concepts et les modèles de variabilité. Dans un second temps, nous illustrons l’utilisation originale de ces structures conceptuelles comme support à des opérations de conception et de recherche d’informations. Enfin, nous élargissons notre champ d’étude aux informations plus complexes définies par des modèles de variabilité qui ont été étendus pour en améliorer l’expressivité, et dont la rétro-ingénierie est encore peu étudiée à ce jour. Nous montrons comment certaines propriétés de l’analyse formelle de concepts permettent de généraliser son utilisation à des descriptions de variantes plus complexes, et étudions son application pour la manipulation d’attributs multivalués et de cardinalités, en complément des caractéristiques booléennes traditionnelles. Nous évaluons notre approche sur des données issues de dépôts tels que SPLOT, fork-insight et de matrices de comparaison de produits de wikipedia. / Software families often rise from reuse practices as cloning existing software products which are then enhanced or pruned to fulfill new requirements. With time, these variants grow in number and in complexity, and become more and more complex to maintain. Software product line engineering gathers a set of methods that aims at facilitating the management and development of such collections of existing variants. Documenting variability is the central point of this paradigm; This variability is represented in variability models that support a large part of software product line engineering processes.The partial or complete migration from software families to a product line approach eases their exploitation.Reverse-engineering, modeling and managing variability are known as crucial tasks of the migration: therefore, numerous methods have been proposed to study descriptions of software families for this goal.Some of them are based on formal concept analysis, a mathematical framework for hierarchical clustering which organises set of objects and their descriptions in canonical structures highlighting naturally their commonalities and variability.In this thesis, we defend that formal concept analysis, more than a tool, is a relevant structural, reusable and extensible framework to study variability of software families.First, we propose an overview of variability information which is highlighted thanks to this framework, and we discuss its scope of applicability.We study the common points between the conceptual structures of formal concept analysis and variability models.Then, we show how to use these conceptual structures to support research and modeling operations.Finally, we broaden the scope of this study to take into account more complex information about extended variability.We evaluate our method on data taken from the SPLOT repository, fork-insight and product comparison matrices from wikipedia.

With the growing number of large data sets, the necessity of complexity reduction applies today more than ever before. Moreover, some data may also be vague or uncertain. Thus, whenever we have an instrument for data analysis, the questions of how to apply complexity reduction methods and how to treat fuzzy data arise rather naturally. In this thesis, we discuss these issues for the very successful data analysis tool Formal Concept Analysis. In fact, we propose different methods for complexity reduction based on qualitative analyses, and we elaborate on various methods for handling fuzzy data. These two topics split the thesis into two parts. Data reduction is mainly dealt with in the first part of the thesis, whereas we focus on fuzzy data in the second part. Although each chapter may be read almost on its own, each one builds on and uses results from its predecessors. The main crosslink between the chapters is given by the reduction methods and fuzzy data. In particular, we will also discuss complexity reduction methods for fuzzy data, combining the two issues that motivate this thesis. / Komplexitätsreduktion ist eines der wichtigsten Verfahren in der Datenanalyse. Mit ständig wachsenden Datensätzen gilt dies heute mehr denn je. In vielen Gebieten stößt man zudem auf vage und ungewisse Daten. Wann immer man ein Instrument zur Datenanalyse hat, stellen sich daher die folgenden zwei Fragen auf eine natürliche Weise: Wie kann man im Rahmen der Analyse die Variablenanzahl verkleinern, und wie kann man Fuzzy-Daten bearbeiten? In dieser Arbeit versuchen wir die eben genannten Fragen für die Formale Begriffsanalyse zu beantworten. Genauer gesagt, erarbeiten wir verschiedene Methoden zur Komplexitätsreduktion qualitativer Daten und entwickeln diverse Verfahren für die Bearbeitung von Fuzzy-Datensätzen. Basierend auf diesen beiden Themen gliedert sich die Arbeit in zwei Teile. Im ersten Teil liegt der Schwerpunkt auf der Komplexitätsreduktion, während sich der zweite Teil der Verarbeitung von Fuzzy-Daten widmet. Die verschiedenen Kapitel sind dabei durch die beiden Themen verbunden. So werden insbesondere auch Methoden für die Komplexitätsreduktion von Fuzzy-Datensätzen entwickelt.

We introduce a new software system called Formal Concept Analysis Research Toolbox (FCART). Our goal is to create a universal integrated environment for knowledge and data engineers. FCART is constructed upon an iterative data analysis methodology and provides a built-in set of research tools based on Formal Concept Analysis techniques for working with object-attribute data representations. The provided toolset allows for the fast integration of extensions on several levels: from internal scripts to plugins. FCART was successfully applied in several data mining and knowledge discovery tasks. Examples of applying the system in medicine and criminal investigations are considered.

Les progrès de la technologie pour la création, le stockage et la diffusion des données ont considérablement augmenté le besoin d’outils qui permettent effectivement aux utilisateurs les moyens d’identifier et de comprendre l’information pertinente. Malgré les possibilités de calcul dans les cadres distribuées telles que des outils comme Hadoop offrent, il a seulement augmenté le besoin de moyens pour identifier et comprendre les informations pertinentes. L’Analyse de Concepts Formels (ACF) peut jouer un rôle important dans ce contexte, en utilisant des moyens plus intelligents dans le processus d’analyse. ACF fournit une compréhension intuitive de la généralisation et de spécialisation des relations entre les objets et leurs attributs dans une structure connue comme un treillis de concepts. Cette thèse aborde le problème de l’exploitation et visualisation des concepts sur un flux de données. L’approche proposée est composé de plusieurs composants distribués qui effectuent le calcul des concepts d’une transaction de base, filtre et transforme les données, les stocke et fournit des fonctionnalités analytiques pour l’exploitation visuelle des données. La nouveauté de notre travail consiste à: (i) une architecture distribuée de traitement et d’analyse des concepts et l’exploitation en temps réel, (ii) la combinaison de l’ACF avec l’analyse des techniques d’exploration, y compris la visualisation des règles d’association, (iii) des nouveaux algorithmes pour condenser et filtrage des données conceptuelles et (iv) un système qui met en œuvre toutes les techniques proposées, Cubix, et ses étude de cas en biologie, dans la conception de systèmes complexes et dans les applications spatiales. / The advances in technology for creation, storage and dissemination of data have dramatically increased the need for tools that effectively provide users with means of identifying and understanding relevant information. Despite the great computing opportunities distributed frameworks such as Hadoop provide, it has only increased the need for means of identifying and understanding relevant information. Formal Concept Analysis (FCA) may play an important role in this context, by employing more intelligent means in the analysis process. FCA provides an intuitive understanding of generalization and specialization relationships among objects and their attributes in a structure known as a concept lattice. The present thesis addresses the problem of mining and visualising concepts over a data stream. The proposed approach is comprised of several distributed components that carry the computation of concepts from a basic transaction, filter and transforms data, stores and provides analytic features to visually explore data. The novelty of our work consists of: (i) a distributed processing and analysis architecture for mining concepts in real-time; (ii) the combination of FCA with visual analytics visualisation and exploration techniques, including association rules analytics; (iii) new algorithms for condensing and filtering conceptual data and (iv) a system that implements all proposed techniques, called Cubix, and its use cases in Biology, Complex System Design and Space Applications.

A Análise de Conceitos Formais (FCA) é uma teoria matemática que formaliza a noção de conceitos e hierarquias conceituais. De importância central a esta teoria é uma estrutura algébrica denominada reticulado de conceitos. Esta estrutura é definida em função de um conjunto de objetos, outro de atributos e uma relação que indica os atributos apresentados por cada objeto. Uma representação gráfica de um reticulado de conceitos, por meio de uma interface computacional, é capaz de expor regularidades presentes em dados a um usuário, e este pode então realizar tarefas de análise exploratória de dados. Este tipo de aplicação de FCA vem sendo empregado em dezenas de projetos pertencentes a áreas diversas, como medicina, serviços de inteligência, engenharia de software e bioinformática. Mostramos neste trabalho um sistema de análise exploratória de dados baseado em FCA, e sua utilização sobre dados reais. Também é mostrado como reticulados de conceitos podem ser empregados em interfaces de recuperação de informação. Do ponto de vista algorítmico, analisamos métodos computacionais para a determinação do reticulado de conceitos, e também de uma subestrutura simplificada, o conjunto de conceitos. O tamanho de um reticulado de conceitos pode ser exponencial em função dos tamanhos dos conjuntos de objetos e de atributos. Assim, é de vital interesse o estabelecimento de cotas superiores para o número de conceitos de um reticulado. Neste trabalho, apresentamos as cotas já conhecidas presentes na literatura. Também estabelecemos uma nova cota superior, e mostramos famílias de casos em que nossa cota superior é mais justa que as demais. Para algumas famílias particulares, nossa cota é polinomial, enquanto que as demais são exponenciais. / Formal Concept Analysis (FCA) is a mathematical theory that formalizes the notion of concepts and conceptual hierarchies. Of central importance to this theory is an algebraic structure termed concept lattice. Such structure becomes defined after being given one set of objects, one of attributes, and an incidence relation describing the attributes held by each object. A graphical representation of a concept lattice, by means of a computational interface, is capable of unfolding regularities present in data to an user, who is then able to conduct exploratory data analysis tasks. This sort of FCA application is currently deployed in tens of projects belonging to a wide range of areas, such as medicine, intelligence services, software engineering and bioinformatics. We show in this work an FCA-based system of exploratory data analysis, and its use over real data. Moreover, it is shown how concept lattices can be employed in information retrieval interfaces. From the algorithmic viewpoint, we analyse computational methods for the determination of a concept lattice, and also of a simplified substructure, the concept set. The size of a concept lattice can be exponential when compared to the size of the objects and the attributes sets. Therefore, it is of paramount interest the establishment of upper bounds for the number of concepts of a lattice. In this work, we present the upper bounds already known in the literature. We also establish a new upper bound, and show families of cases in which our bound is sharper than the others. For particular families, our bound is polynomial, whereas the other bounds are exponential.

Appliqué à des problèmes actuels de recherche pharmaceutique, ce mémoire traite de la génération de signatures de biomarqueurs par une approche d'extraction de règles d'association et une Analyse Formelle de Concepts. Elle a aboutit au développement d'une méthodologie qui a été validée par six projets de recherche de signatures de biomarqueurs.Alors qu'il n'existe pas de méthode optimale pour traiter les données biomarqueurs, cette méthodologie logique s'appuie sur un scénario global d'analyse déployant quatre méthodes, chacune dépendante de procédés différents. Cette architecture qualifie une problématique centrale de manière à optimiser la qualité d'une solution aux différents problèmes scientifiques posés. Les six applications pratiques ont démontré l'intérêt de la prise en compte précoce des critères de qualité énoncés par les experts du domaine. L'interactivité est soutenue tout au long du processus de découverte et produit des résultats imprévus pour l'expert. La méthodologie s'inscrit dans la lignée des approches dédiées à la stratification systématique des individus, qui constitue le premier palier vers une médecine personnalisée. / In the framework of current intricate questions to be solved by the pharmaceutical industry, this manuscript examines the generation of biomarker signatures through an approach that combines association rules extraction and Formal Concept Analysis. It led to the development of a methodology which was validated by six research industrial projects. While there is no single optimal method to handle biomarkers datasets, this logical methodology relies on a global datamining scenario made up of four different methods. Each method utilizes different processes. This architecture qualifies global approach that helps to optimize a response to different biomarker signatures discovery problems. The six applications presented in this manuscript demonstrate the interest of an early consideration of the quality criteria are expressed by the experts in the field. The interactivity is supported throughout the process of discovery and produces unexpected results for the expert. The methodology helps the systematic stratification of individuals, which constitutes the first step towards personalized medicine.

The aim of this dissertation is to provide a unified treatment of various spell checkers and correctors. Firstly, the spell checking and correcting problems are formally described in mathematics in order to provide a better understanding of these tasks. An approach that is similar to the way in which denotational semantics used to describe programming languages is adopted. Secondly, the various attributes of existing spell checking and correcting techniques are discussed. Extensive studies on selected spell checking/correcting algorithms and packages are then performed. Lastly, an empirical investigation of various spell checking/correcting packages is presented. It provides a comparison and suggests a classification of these packages in terms of their functionalities, implementation strategies, and performance. The investigation was conducted on packages for spell checking and correcting in English as well as in Northern Sotho and Chinese. The classification provides a unified presentation of the strengths and weaknesses of the techniques studied in the research. The findings provide a better understanding of these techniques in order to assist in improving some existing spell checking/correcting applications and future spell checking/correcting package designs and implementations. / Dissertation (MSc)--University of Pretoria, 2009. / Computer Science / unrestricted

Description logics knowledge bases are a popular approach to represent terminological and assertional knowledge suitable for computers to work with. Despite that, the practicality of description logics is impaired by the difficulties one has to overcome to construct such knowledge bases. Previous work has addressed this issue by providing methods to learn valid terminological knowledge from data, making use of ideas from formal concept analysis. A basic assumption here is that the data is free of errors, an assumption that can in general not be made for practical applications. This thesis presents extensions of these results that allow to handle errors in the data. For this, knowledge that is "almost valid" in the data is retrieved, where the notion of "almost valid" is formalized using the notion of confidence from data mining. This thesis presents two algorithms which achieve this retrieval. The first algorithm just extracts all almost valid knowledge from the data, while the second algorithm utilizes expert interaction to distinguish errors from rare but valid counterexamples.

With the growing number of large data sets, the necessity of complexity reduction applies today more than ever before. Moreover, some data may also be vague or uncertain. Thus, whenever we have an instrument for data analysis, the questions of how to apply complexity reduction methods and how to treat fuzzy data arise rather naturally. In this thesis, we discuss these issues for the very successful data analysis tool Formal Concept Analysis. In fact, we propose different methods for complexity reduction based on qualitative analyses, and we elaborate on various methods for handling fuzzy data. These two topics split the thesis into two parts. Data reduction is mainly dealt with in the first part of the thesis, whereas we focus on fuzzy data in the second part. Although each chapter may be read almost on its own, each one builds on and uses results from its predecessors. The main crosslink between the chapters is given by the reduction methods and fuzzy data. In particular, we will also discuss complexity reduction methods for fuzzy data, combining the two issues that motivate this thesis. / Komplexitätsreduktion ist eines der wichtigsten Verfahren in der Datenanalyse. Mit ständig wachsenden Datensätzen gilt dies heute mehr denn je. In vielen Gebieten stößt man zudem auf vage und ungewisse Daten. Wann immer man ein Instrument zur Datenanalyse hat, stellen sich daher die folgenden zwei Fragen auf eine natürliche Weise: Wie kann man im Rahmen der Analyse die Variablenanzahl verkleinern, und wie kann man Fuzzy-Daten bearbeiten? In dieser Arbeit versuchen wir die eben genannten Fragen für die Formale Begriffsanalyse zu beantworten. Genauer gesagt, erarbeiten wir verschiedene Methoden zur Komplexitätsreduktion qualitativer Daten und entwickeln diverse Verfahren für die Bearbeitung von Fuzzy-Datensätzen. Basierend auf diesen beiden Themen gliedert sich die Arbeit in zwei Teile. Im ersten Teil liegt der Schwerpunkt auf der Komplexitätsreduktion, während sich der zweite Teil der Verarbeitung von Fuzzy-Daten widmet. Die verschiedenen Kapitel sind dabei durch die beiden Themen verbunden. So werden insbesondere auch Methoden für die Komplexitätsreduktion von Fuzzy-Datensätzen entwickelt.