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2016 | Buch

Concept lattices Kapitel lesen Erstes Kapitel lesen

Conceptual Exploration

verfasst von: Bernhard Ganter, Sergei Obiedkov

Verlag: Springer Berlin Heidelberg

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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SUCHEN

Über dieses Buch

This is the first textbook on attribute exploration, its theory, its algorithms forapplications, and some of its many possible generalizations. Attribute explorationis useful for acquiring structured knowledge through an interactive process, byasking queries to an expert. Generalizations that handle incomplete, faulty, orimprecise data are discussed, but the focus lies on knowledge extraction from areliable information source.The method is based on Formal Concept Analysis, a mathematical theory ofconcepts and concept hierarchies, and uses its expressive diagrams. The presentationis self-contained. It provides an introduction to Formal Concept Analysiswith emphasis on its ability to derive algebraic structures from qualitative data,which can be represented in meaningful and precise graphics.

Inhaltsverzeichnis

Frontmatter
Chapter 1. Concept lattices
Abstract
This book is about attribute exploration, a simple but useful knowledge acquisition technique from Formal Concept Analysis (FCA). The latter is a mathematical theory of concepts and conceptual hierarchies, called concept lattices. FCA offers several highly practical methods for working with concrete qualitative data. A solid knowledge of FCA is not a prerequisite for attribute exploration, but knowing the basic ideas will help. We therefore start with an introduction.
Bernhard Ganter, Sergei Obiedkov
Chapter 2. An algorithm for closure systems
Abstract
The knowledge acquisition algorithm that is the central theme of our book can most naturally be phrased in the language of Formal Concept Analysis. It essentially relies on a single property of concept lattices, namely, that the set of concept intents is closed under intersection. The technique works for an arbitrary intersection-closed family of sets, that is, for a closure system. Readers who are familiar with closure systems but not with Formal Concept Analysis may prefer this approach.
Bernhard Ganter, Sergei Obiedkov
Chapter 3. The canonical basis
Abstract
Have another look at the concept lattice shown in Figure 1.11 (p. 14). The six attributes describe how two unit squares can be placed with respect to each other. Each of the ten objects is a pair of unit squares representing a possible placement. These ten pairs are representatives for an infinite set of possible positions that such pairs of squares may have. It is not stated, but perhaps expected by the reader, that these ten examples cover all possible combinations of the given attributes.
Bernhard Ganter, Sergei Obiedkov
Chapter 4. Attribute exploration
Abstract
Have another look at the canonical basis in Figure 3.2 (p. 97), which was computed for the context of triangles. The implications in this set are obviously true, because they hold for all triangles, not only for the objects of the triangles context on page 23. This information is important, because it shows that the concept lattice given in Figure 1.16 (p. 27) will not change if more examples are added. The triangles in the formal context are representative of the entire theory. The canonical basis generates the implication theory of these five attributes for all triangles. Every implication that holds for all triangles follows from the canonical basis. For every implication that does not hold in general, there is already a counterexample among the seven triangles of the formal context.
Bernhard Ganter, Sergei Obiedkov
Chapter 5. Exploring data tables
Abstract
In this chapter we extend attribute exploration by allowing for “non-implicational” background knowledge. This is propositional background knowledge that is not as “harmless” as the background implications of Section 4.3.2.
Bernhard Ganter, Sergei Obiedkov
Chapter 6. More expressive variants of exploration
Abstract
Several authors have extended the basic method of attribute exploration, as it is presented in the two previous chapters of this book, to more advanced situations, and this last chapter is devoted to such ideas. We start with rule exploration, which lifts attribute exploration in a rather naturalway to first-order predicate logic, with Horn formulas replacing implications. Next we discuss how attribute exploration can be integrated with Description Logics. However, so much substantial research has been contributed to this topic thatwe can only introduce some first ideas. The third section is devoted to concept exploration, which was already mentioned in the very first publication on Formal Concept Analysis. Three more generalizations are sketched in the fourth section, which then concludes by mentioning a few further ones.
Bernhard Ganter, Sergei Obiedkov
Backmatter
Metadaten
Titel
Conceptual Exploration
verfasst von
Bernhard Ganter
Sergei Obiedkov
Copyright-Jahr
2016
Verlag
Springer Berlin Heidelberg
Electronic ISBN
978-3-662-49291-8
Print ISBN
978-3-662-49290-1
DOI
https://doi.org/10.1007/978-3-662-49291-8