The theory and practice of coupling formal concept analysis to relational databases (original) (raw)
Related papers
2008
The theory of Formal Concept Analysis offers an algebraic approach to data analysis and knowledge processing. The notion of dependencies between attributes in a many-valued context has been introduced in [3], by Ganter and Wille. J. Hereth (2002) introduces the power context family resulting from the canonical translation of a relational database. Regarding to this power context family, he defines the formal context of functional dependencies. In this context, implications hold for functional dependencies. We propose a software tool, which constructs the formal context of functional dependencies, and it builds the concept lattice and determines the implications in the context, which syntactically are the same as functional dependencies in the analyzed table. The software can be used in relational database design and for detecting functional dependencies in existing tables, respectively.
A software tool for data analysis based on formal concept analysis
Formal Concept Analysis is a useful tool to represent logi-cal implications in datasets, to analyze the underground knowledge that lies behind large amounts of data. A database relation can be seen as a many-valued context [3]. J. Hereth in [4] introduces the formal context of functional dependencies. In this context, implications hold for functional dependencies. We develop a software application that analyzes an existing relational data table and detect functional dependencies in it. The user can choose to analyze a table from a MS SQL Server, Oracle or MySQL database and the software will build the formal context of functional depen-dencies. We use Conexp [6] to build the concept lattice and implications in this context. These implications will be the functional dependencies for the analyzed table. Having the functional dependencies, we can detect candidate keys and we can decide if the table is in 2NF or 3NF or BCNF. To our knowledge, this method was not implemented yet.
The Lattice of Concept Graphs of a Relationally Scaled Context
Lecture Notes in Computer Science, 1999
The aim of this paper is to contribute to Data Analysis by clarifying how concept graphs may be derived from data tables. First it is shown how, by the method of relational scaling, a many-valued data context can be transformed into a power context family. Then it is proved that the concept graphs of a power context family form a lattice which can be described as a subdirect product of speci c intervals of the concept lattices of the power context family (each extended by a new top-element). How this may become practical is demonstrated using a data table about the domestic ights in Austria. Finally, the lattice of syntactic concept graphs over an alphabet of object, concept, and relation names is determined and related to the lattices of concept graphs of the power context families which are semantic models of the given contextual syntax.
Logical scaling in formal concept analysis
Lecture Notes in Computer Science, 1997
Logical scaling is a new method to transform data matrices which are based on object-attribute-value-relationships into data matrices from which conceptual hierarchies can be explored. The derivation of concept lattices is determined by terminologies expressed in a formallogical language.
A Proposal for Combining Formal Concept Analysis and Description Logics for Mining Relational Data
Lecture Notes in Computer Science, 2007
Recent advances in data and knowledge engineering have emphasized the need for formal concept analysis (FCA) tools taking into account structured data. There are a few adaptations of the classical FCA methodology for handling contexts holding on complex data formats, e.g. graph-based or relational data. In this paper, relational concept analysis (RCA) is proposed, as an adaptation of FCA for analyzing objects described both by binary and relational attributes. The RCA process takes as input a collection of contexts and of inter-context relations, and yields a set of lattices, one per context, whose concepts are linked by relations. Moreover, a way of representing the concepts and relations extracted with RCA is proposed in the framework of a description logic. The RCA process has been implemented within the Galicia platform, offering new and efficient tools for knowledge and software engineering.