Status, Abstract

Gunther Schmidt

Theory Extraction in Relational Data Analysis

.pdf .bib

Has appeared as contribution pp. 68-86 to
Harrie de Swart, Ewa Orlowska, Marc Roubens, Gunther Schmidt (eds.):
Relational Methods in Computer Science, Lect. Notes in Comput. Science 2929
ISSN 0302-9743, ISBN 3-540-20780-5

Department of Computing Science
University of the Federal Armed Forces Munich
85577 Neubiberg, Germany

September 2003
From numerical mathematics we know that a linear equation Ax = b may be solved more efficiently if a reduction of A is known beforehand. Having 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 a report, 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.