提供方

National Research University Higher School of Economics

課程信息

4.8

19 ratings

•

7 reviews

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....

立即開始，按照自己的計劃學習。

根據您的日程表重置截止日期。

完成時間大約為36 小時

字幕：English

立即開始，按照自己的計劃學習。

根據您的日程表重置截止日期。

完成時間大約為36 小時

字幕：English

章節

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 個視頻（共 66 分鐘）, 1 個閱讀材料, 2 個測驗

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

Further reading10分鐘

Reading concept lattice diagrams分鐘

Formal concepts and closure operators分鐘

章節

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 個視頻（共 98 分鐘）, 3 個測驗

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

Supremum and infimum30分鐘

Lattices and complete lattices分鐘

Clarification and reduction分鐘

章節

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 個視頻（共 121 分鐘）, 3 個測驗

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

Transposed context30分鐘

Closures in lectic order分鐘

Implications分鐘

章節

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 個視頻（共 67 分鐘）, 3 個測驗

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

Implications and pseudo-intents分鐘

Canonical basis分鐘

Functional dependencies分鐘

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.

What is the refund policy?

Is financial aid available?

還有其他問題嗎？請訪問 學生幫助中心。