Об этом курсе
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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

Промежуточный уровень

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Предполагаемая нагрузка: 6 weeks, 4-6 hours per week

Прибл. 37 ч. на завершение
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English

Субтитры: English
Globe

Только онлайн-курсы

Начните сейчас и учитесь по собственному графику.
Calendar

Гибкие сроки

Назначьте сроки сдачи в соответствии со своим графиком.
Intermediate Level

Промежуточный уровень

Clock

Предполагаемая нагрузка: 6 weeks, 4-6 hours per week

Прибл. 37 ч. на завершение
Comment Dots

English

Субтитры: English

Программа курса: что вы изучите

1

Раздел
Clock
4 ч. на завершение

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 видео (всего 66 мин.), 1 материал для самостоятельного изучения, 2 тестов
Video14 видео
What is formal concept analysis?4мин
Understanding the concept lattice diagram2мин
Reading concepts from the lattice diagram4мин
Reading implications from the lattice diagram5мин
Conceptual clustering6мин
Formal contexts and derivation operators8мин
Formal concepts2мин
Closure operators9мин
Closure systems2мин
Software: Concept Explorer7мин
Many-valued contexts4мин
Conceptual scaling schemas3мин
Scaling ordinal data3мин
Reading1 материал для самостоятельного изучения
Further reading10мин
Quiz2 практического упражнения
Reading concept lattice diagramsмин
Formal concepts and closure operatorsмин

2

Раздел
Clock
4 ч. на завершение

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 видео (всего 98 мин.), 3 тестов
Video8 видео
Supremum and infimum15мин
Lattices9мин
The basic theorem (I)11мин
The basic theorem (II)12мин
Line diagrams13мин
Context clarification and reduction12мин
Context reduction: an example11мин
Quiz3 практического упражнения
Supremum and infimum30мин
Lattices and complete latticesмин
Clarification and reductionмин

3

Раздел
Clock
5 ч. на завершение

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 видео (всего 121 мин.), 3 тестов
Video13 видео
Drawing a concept lattice diagram4мин
A naive algorithm for enumerating closed sets2мин
Representing sets by bit vectors4мин
Closures in lectic order10мин
Next Closure through an example10мин
The complexity of the algorithm13мин
Basic incremental strategy14мин
An example10мин
The definition of implications10мин
Examples of attribute implications7мин
Implication inference12мин
Computing the closure under implications7мин
Quiz3 практического упражнения
Transposed context30мин
Closures in lectic orderмин
Implicationsмин

4

Раздел
Clock
4 ч. на завершение

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 видео (всего 67 мин.), 3 тестов
Video9 видео
Pseudo-closed sets and canonical basis12мин
Preclosed sets8мин
Preclosure operator6мин
Computing the canonical basis4мин
An example5мин
Complexity issues8мин
Functional dependencies8мин
Translation between functional dependencies and implications5мин
Quiz3 практического упражнения
Implications and pseudo-intentsмин
Canonical basisмин
Functional dependenciesмин

Преподаватель

Sergei Obiedkov

Associate Professor
Faculty of computer science

О 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...

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