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.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 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) \(\theta \).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this chapter
Cite this chapter
Hońko, P. (2017). Properties of Granular-Relational Data Mining Framework. In: Granular-Relational Data Mining. Studies in Computational Intelligence, vol 702. Springer, Cham. https://doi.org/10.1007/978-3-319-52751-2_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-52751-2_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-52750-5
Online ISBN: 978-3-319-52751-2
eBook Packages: EngineeringEngineering (R0)