proposé par

National Research University Higher School of Economics

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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....

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Réinitialisez les dates limites selon votre disponibilité.

Approx. 36 heures pour terminer

Sous-titres : English

Commencez dès maintenant et apprenez aux horaires qui vous conviennent.

Réinitialisez les dates limites selon votre disponibilité.

Approx. 36 heures pour terminer

Sous-titres : English

Section

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....

14 vidéos (Total 66 min), 1 lecture, 2 quiz

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

Further reading10 min

Reading concept lattice diagrams min

Formal concepts and closure operators min

Section

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....

8 vidéos (Total 98 min), 3 quiz

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

Supremum and infimum30 min

Lattices and complete lattices min

Clarification and reduction min

Section

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....

13 vidéos (Total 121 min), 3 quiz

Finding the concepts12 min

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

Transposed context30 min

Closures in lectic order min

Implications min

Section

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....

9 vidéos (Total 67 min), 3 quiz

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

Implications and pseudo-intents min

Canonical basis min

Functional dependencies min

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...

When will I have access to the lectures and assignments?

Once you enroll for a Certificate, you’ll have access to all videos, quizzes, and programming assignments (if applicable). Peer review assignments can only be submitted and reviewed once your session has begun. If you choose to explore the course without purchasing, you may not be able to access certain assignments.

What will I get if I purchase the Certificate?

When you purchase a Certificate you get access to all course materials, including graded assignments. Upon completing the course, your electronic Certificate will be added to your Accomplishments page - from there, you can print your Certificate or add it to your LinkedIn profile. If you only want to read and view the course content, you can audit the course for free.

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