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#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 37 hours to complete

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

#### English

Subtitles: English

#### 100% online

Start instantly and learn at your own schedule.

#### Approx. 37 hours to complete

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

#### English

Subtitles: English

### Syllabus - What you will learn from this course

Week
1
4 hours to complete

## 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....
14 videos (Total 66 min), 1 reading, 2 quizzes
14 videos
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
2 practice exercises
Week
2
4 hours to complete

## 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....
8 videos (Total 98 min), 3 quizzes
8 videos
Supremum and infimum15m
Lattices9m
The basic theorem (I)11m
The basic theorem (II)12m
Line diagrams13m
Context clarification and reduction12m
Context reduction: an example11m
3 practice exercises
Supremum and infimum30m
Lattices and complete latticess
Clarification and reductions
Week
3
5 hours to complete

## 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....
13 videos (Total 121 min), 3 quizzes
13 videos
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
3 practice exercises
Transposed context30m
Closures in lectic orders
Implicationss
Week
4
4 hours to complete

## 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....
9 videos (Total 67 min), 3 quizzes
9 videos
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
3 practice exercises
Implications and pseudo-intentss
Canonical basiss
Functional dependenciess

## Instructor

### Sergei Obiedkov

Associate Professor
Faculty of computer science

## About 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...