Paper Info
Title
Theory Extraction in Relational Data Analysis
Abstract
� c d � , one will solve By = c first and then Dz = d − Cy .H aving an a priori knowledge of this kind is also an advantage in many other application fields. We here deal with a diversity of techniques to decompose relations according to some criteria and embed these techniques in a common framework. The results of decompositions obtained may be used in decision making, but also as a support for teaching, as they often give visual help. Our starting point will always be a concretely given relation, i.e., a Boolean matrix. In most cases, we will look for a partition of the set of rows and the set of columns, respectively, that arises from some algebraic condition. From these partitions, a rearranged matrix making these partitions easily visible shall be computed as well as the permutation matrix necessary to achieve this. The current article presents results of the report (Sch02) obtainable via http://ist.unibw-muenchen.de/People/schmidt/DecompoHomePage.html which gives a detailed account of the topic. The report is not just a research report but also a Haskell program in literate style. In contrast, the present article only gives hints as to these programs. Therefore, some details are omitted. This article is organized as follows. Chapter 2 presents the idea of extracting theories as proposed in this paper. Then Ch. 3 will mention some prerequisites. The hints concerning the relational language used are given in Ch. 4, followed by Ch. 5 with models and interpretations in Haskell. With Ch. 6 the first de- composition based on the strongly connected component ontology is elaborated in some detail to further clarify the idea. Theoretical basics of the more sophisti- cated Galois decompositions are explained in Ch. 7 before these are made ready for programming in Ch. 8. 1 Cooperation and communication around this research was partly sponsored by the European COST Action 274: TARSKI (Theory and Application of Relational Struc- tures as Knowledge Instruments), which is gratefully acknowledged.
Year
DOI
Venue
2003
10.1007/978-3-540-24615-2_4
LECTURE NOTES IN COMPUTER SCIENCE
Keywords
Field
DocType
� =,a priori knowledge,strongly connected component,relational data
Discrete mathematics,Linear equation,Logical matrix,Relational database,Computer science,Universal relation,A priori and a posteriori,Numerical mathematics
Conference
Volume
ISSN
Citations 
2929
0302-9743
0
PageRank 
References 
Authors
0.34
1
1
Name
Order
Citations
PageRank
Gunther Schmidt120330.70