Offered By

National Research University Higher School of Economics

About this Course

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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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Suggested: 6 weeks, 4-6 hours per week...

Subtitles: English

Start instantly and learn at your own schedule.

Reset deadlines in accordance to your schedule.

Suggested: 6 weeks, 4-6 hours per week...

Subtitles: English

Week

1This 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 videos (Total 66 min), 1 reading, 2 quizzes

What is formal concept analysis?4m

Understanding the concept lattice diagram2m

Reading concepts from the lattice diagram4m

Reading implications from the lattice diagram5m

Conceptual clustering6m

Formal contexts and derivation operators8m

Formal concepts2m

Closure operators9m

Closure systems2m

Software: Concept Explorer7m

Many-valued contexts4m

Conceptual scaling schemas3m

Scaling ordinal data3m

Further reading10m

Reading concept lattice diagramss

Formal concepts and closure operatorss

Week

2This 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 videos (Total 98 min), 3 quizzes

Supremum and infimum15m

Lattices9m

The basic theorem (I)11m

The basic theorem (II)12m

Line diagrams13m

Context clarification and reduction12m

Context reduction: an example11m

Supremum and infimum30m

Lattices and complete latticess

Clarification and reductions

Week

3We 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 videos (Total 121 min), 3 quizzes

Drawing a concept lattice diagram4m

A naive algorithm for enumerating closed sets2m

Representing sets by bit vectors4m

Closures in lectic order10m

Next Closure through an example10m

The complexity of the algorithm13m

Basic incremental strategy14m

An example10m

The definition of implications10m

Examples of attribute implications7m

Implication inference12m

Computing the closure under implications7m

Transposed context30m

Closures in lectic orders

Implicationss

Week

4This 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 videos (Total 67 min), 3 quizzes

Pseudo-closed sets and canonical basis12m

Preclosed sets8m

Preclosure operator6m

Computing the canonical basis4m

An example5m

Complexity issues8m

Functional dependencies8m

Translation between functional dependencies and implications5m

Implications and pseudo-intentss

Canonical basiss

Functional dependenciess

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 communicamathematics, engineering, and more.
Learn more on www.hse.ru...

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