À propos de ce cours
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This course is an introduction into formal concept analysis (FCA), a mathematical theory oriented at applications in knowledge representation, knowledge acquisition, data analysis and visualization. It provides tools for understanding the data by representing it as a hierarchy of concepts or, more exactly, a concept lattice. FCA can help in processing a wide class of data types providing a framework in which various data analysis and knowledge acquisition techniques can be formulated. In this course, we focus on some of these techniques, as well as cover the theoretical foundations and algorithmic issues of FCA. Upon completion of the course, the students will be able to use the mathematical techniques and computational tools of formal concept analysis in their own research projects involving data processing. Among other things, the students will learn about FCA-based approaches to clustering and dependency mining. The course is self-contained, although basic knowledge of elementary set theory, propositional logic, and probability theory would help. End-of-the-week quizzes include easy questions aimed at checking basic understanding of the topic, as well as more advanced problems that may require some effort to be solved....
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Intermediate Level

Niveau intermédiaire

Clock

Recommandé : 6 weeks, 4-6 hours per week

Approx. 36 heures pour terminer
Comment Dots

English

Sous-titres : English
Globe

Cours en ligne à 100 %

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.
Calendar

Dates limites flexibles

Réinitialisez les dates limites selon votre disponibilité.
Intermediate Level

Niveau intermédiaire

Clock

Recommandé : 6 weeks, 4-6 hours per week

Approx. 36 heures pour terminer
Comment Dots

English

Sous-titres : English

Programme du cours : ce que vous apprendrez dans ce cours

1

Section
Clock
4 heures pour terminer

Formal concept analysis in a nutshell

This week we will learn the basic notions of formal concept analysis (FCA). We'll talk about some of its typical applications, such as conceptual clustering and search for implicational dependencies in data. We'll see a few examples of concept lattices and learn how to interpret them. The simplest data structure in formal concept analysis is the formal context. It is used to describe objects in terms of attributes they have. Derivation operators in a formal context link together object and attribute subsets; they are used to define formal concepts. They also give rise to closure operators, and we'll talk about what these are, too. We'll have a look at software called Concept Explorer, which is good for basic processing of formal contexts. We'll also talk a little bit about many-valued contexts, where attributes may have many values. Conceptual scaling is used to transform many-valued contexts into "standard", one-valued, formal contexts....
Reading
14 vidéos (Total 66 min), 1 lecture, 2 quiz
Video14 vidéos
What is formal concept analysis?4 min
Understanding the concept lattice diagram2 min
Reading concepts from the lattice diagram4 min
Reading implications from the lattice diagram5 min
Conceptual clustering6 min
Formal contexts and derivation operators8 min
Formal concepts2 min
Closure operators9 min
Closure systems2 min
Software: Concept Explorer7 min
Many-valued contexts4 min
Conceptual scaling schemas3 min
Scaling ordinal data3 min
Reading1 lecture
Further reading10 min
Quiz2 exercices pour s'entraîner
Reading concept lattice diagrams min
Formal concepts and closure operators min

2

Section
Clock
4 heures pour terminer

Concept lattices and their line diagrams

This week we'll talk about some mathematical properties of concepts. We'll define a partial order on formal concepts, that of "being less general". Ordered in this way, the concepts of a formal concept constitute a special mathematical structure, a complete lattice. We'll learn what these are, and we'll see, through the basic theorem on concept lattices, that any complete lattice can, in a certain sense, be modelled by a formal context. We'll also discuss how a formal context can be simplified without loosing the structure of its concept lattice....
Reading
8 vidéos (Total 98 min), 3 quiz
Video8 vidéos
Supremum and infimum15 min
Lattices9 min
The basic theorem (I)11 min
The basic theorem (II)12 min
Line diagrams13 min
Context clarification and reduction12 min
Context reduction: an example11 min
Quiz3 exercices pour s'entraîner
Supremum and infimum30 min
Lattices and complete lattices min
Clarification and reduction min

3

Section
Clock
5 heures pour terminer

Constructing concept lattices

We will consider a few algorithms that build the concept lattice of a formal context: a couple of naive approaches, which are easy to use if one wants to build the concept lattice of a small context; a more sophisticated approach, which enumerates concepts in a specific order; and an incremental strategy, which can be used to update the concept lattice when a new object is added to the context. We will also give a formal definition of implications, and we'll see how an implication can logically follow from a set of other implications....
Reading
13 vidéos (Total 121 min), 3 quiz
Video13 vidéos
Drawing a concept lattice diagram4 min
A naive algorithm for enumerating closed sets2 min
Representing sets by bit vectors4 min
Closures in lectic order10 min
Next Closure through an example10 min
The complexity of the algorithm13 min
Basic incremental strategy14 min
An example10 min
The definition of implications10 min
Examples of attribute implications7 min
Implication inference12 min
Computing the closure under implications7 min
Quiz3 exercices pour s'entraîner
Transposed context30 min
Closures in lectic order min
Implications min

4

Section
Clock
4 heures pour terminer

Implications

This week we'll continue talking about implications. We'll see that implication sets can be redundant, and we'll learn to summarise all valid implications of a formal context by its canonical (Duquenne–Guigues) basis. We'll study one concrete algorithm that computes the canonical basis, which turns out to be a modification of the Next Closure algorithm from the previous week. We'll also talk about what is known in database theory as functional dependencies, and we'll show how they are related to implications....
Reading
9 vidéos (Total 67 min), 3 quiz
Video9 vidéos
Pseudo-closed sets and canonical basis12 min
Preclosed sets8 min
Preclosure operator6 min
Computing the canonical basis4 min
An example5 min
Complexity issues8 min
Functional dependencies8 min
Translation between functional dependencies and implications5 min
Quiz3 exercices pour s'entraîner
Implications and pseudo-intents min
Canonical basis min
Functional dependencies min

Enseignant

Sergei Obiedkov

Associate Professor
Faculty of computer science

À propos de National Research University Higher School of Economics

National Research University - Higher School of Economics (HSE) is one of the top research universities in Russia. Established in 1992 to promote new research and teaching in economics and related disciplines, it now offers programs at all levels of university education across an extraordinary range of fields of study including business, sociology, cultural studies, philosophy, political science, international relations, law, Asian studies, media and communications, IT, mathematics, engineering, and more. Learn more on www.hse.ru...

Foire Aux Questions

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