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2017 | OriginalPaper | Chapter

3. Properties of Granular-Relational Data Mining Framework

Author : Piotr Hońko

Published in: Granular-Relational Data Mining

Publisher: Springer International Publishing

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Abstract

This chapter investigates properties of the general granular computing based framework for mining relational data. The properties enable to define the generality relation on the set of alternative granular representations of relational data. This chapter also discusses the usefulness of the properties in tasks such as relational objects representation, search space limitation, and relational patterns generation.

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previous chapter Information System for Relational Data
next chapter Association Discovery and Classification Rule Mining
Footnotes
1
If the depth level for objects representation is i, then those for the remaining tasks may be not higher than i.
 
2
Learning from interpretations [19] is an alternative way of handling relational data. Interpretations correspond to non-abstract objects representations introduced in Chap. 2.
 
3
Proofs of the propositions formulated in this chapter can be found in [44].
 
4
One should distinguish between the syntax of a related set and the syntactical comparison of related sets. The former concerns the form of the related set, whereas the latter does the way the relate sets are compared. Analogously for semantics.
 
5
Two substitutions are equivalent if and only if each one can be obtained from the other one by renaming variables.
 
6
The notion of substitution is used in two cases: for the generalization of related sets; for the semantic comparison of generalized related sets. To better distinguish these cases, we denote the former substitution by (indexed) \(\sigma \), and the latter one by (indexed) \(\theta \).
 
Metadata
Title
Properties of Granular-Relational Data Mining Framework
Author
Piotr Hońko
Copyright Year
2017
Book
Granular-Relational Data Mining

Print ISBN: 978-3-319-52750-5

Electronic ISBN: 978-3-319-52751-2

Copyright Year: 2017

DOI
https://doi.org/10.1007/978-3-319-52751-2_3

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