課程信息
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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

中級

Clock

建議:6 weeks, 4-6 hours per week

完成時間大約為36 小時
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English

字幕:English
Globe

100% 在線課程

立即開始,按照自己的計劃學習。
Calendar

可靈活調整截止日期

根據您的日程表重置截止日期。
Intermediate Level

中級

Clock

建議:6 weeks, 4-6 hours per week

完成時間大約為36 小時
Comment Dots

English

字幕:English

教學大綱 - 您將從這門課程中學到什麼

1

章節
Clock
完成時間為 4 小時

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 個視頻(共 66 分鐘), 1 個閱讀材料, 2 個測驗
Video14 個視頻
What is formal concept analysis?4分鐘
Understanding the concept lattice diagram2分鐘
Reading concepts from the lattice diagram4分鐘
Reading implications from the lattice diagram5分鐘
Conceptual clustering6分鐘
Formal contexts and derivation operators8分鐘
Formal concepts2分鐘
Closure operators9分鐘
Closure systems2分鐘
Software: Concept Explorer7分鐘
Many-valued contexts4分鐘
Conceptual scaling schemas3分鐘
Scaling ordinal data3分鐘
Reading1 個閱讀材料
Further reading10分鐘
Quiz2 個練習
Reading concept lattice diagrams分鐘
Formal concepts and closure operators分鐘

2

章節
Clock
完成時間為 4 小時

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 個視頻(共 98 分鐘), 3 個測驗
Video8 個視頻
Supremum and infimum15分鐘
Lattices9分鐘
The basic theorem (I)11分鐘
The basic theorem (II)12分鐘
Line diagrams13分鐘
Context clarification and reduction12分鐘
Context reduction: an example11分鐘
Quiz3 個練習
Supremum and infimum30分鐘
Lattices and complete lattices分鐘
Clarification and reduction分鐘

3

章節
Clock
完成時間為 5 小時

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 個視頻(共 121 分鐘), 3 個測驗
Video13 個視頻
Drawing a concept lattice diagram4分鐘
A naive algorithm for enumerating closed sets2分鐘
Representing sets by bit vectors4分鐘
Closures in lectic order10分鐘
Next Closure through an example10分鐘
The complexity of the algorithm13分鐘
Basic incremental strategy14分鐘
An example10分鐘
The definition of implications10分鐘
Examples of attribute implications7分鐘
Implication inference12分鐘
Computing the closure under implications7分鐘
Quiz3 個練習
Transposed context30分鐘
Closures in lectic order分鐘
Implications分鐘

4

章節
Clock
完成時間為 4 小時

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 個視頻(共 67 分鐘), 3 個測驗
Video9 個視頻
Pseudo-closed sets and canonical basis12分鐘
Preclosed sets8分鐘
Preclosure operator6分鐘
Computing the canonical basis4分鐘
An example5分鐘
Complexity issues8分鐘
Functional dependencies8分鐘
Translation between functional dependencies and implications5分鐘
Quiz3 個練習
Implications and pseudo-intents分鐘
Canonical basis分鐘
Functional dependencies分鐘

講師

Sergei Obiedkov

Associate Professor
Faculty of computer science

關於 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...

常見問題

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