Introduction to Formal Concept Analysis

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课程简介

Higher School of Economics

课程大纲

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.

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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. Do you have technical problems? Write to us: coursera@hse.ru

形式概念分析简介:本课程是形式概念分析(FCA)的简介,后者是一种面向知识表示,知识获取,数据分析和可视化应用的数学理论。它通过将数据表示为概念的层次结构或更确切地说是概念格来提供理解数据的工具。 FCA可以帮助处理各种各样的数据类型,从而提供一个框架,可以在其中制定各种数据分析和知识获取技术。在本课程中,我们将重点介绍其中的一些技术,并涵盖FCA的理论基础和算法问题。 完成课程后,学生将能够在自己的涉及数据处理的研究项目中使用形式概念分析的数学技术和计算工具。除其他事项外,学生还将学习基于FCA的聚类和依赖挖掘方法。 该课程是独立的,尽管基本集理论,命题逻辑和概率论的基础知识会有所帮助。 周末测验包括旨在检查对主题的基本理解的简单问题,以及可能需要付出一些努力才能解决的更高级的问题。 你有技术上的问题吗?写信给我们:coursera@hse.ru

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