Mining Data with Group Theoretical Means

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Author(s): Gabriele Kern-Isberner (University of Dortmund, Germany)
Copyright: 2009
Pages: 5
Source title: Encyclopedia of Data Warehousing and Mining, Second Edition
Source Author(s)/Editor(s): John Wang (Montclair State University, USA)
DOI: 10.4018/978-1-60566-010-3.ch195

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Abstract

Knowledge discovery refers to the process of extracting new, interesting, and useful knowledge from data and presenting it in an intelligible way to the user. Roughly, knowledge discovery can be considered a three-step process: preprocessing data; data mining, in which the actual exploratory work is done; and interpreting the results to the user. Here, I focus on the data-mining step, assuming that a suitable set of data has been chosen properly. The patterns that we search for in the data are plausible relationships, which agents may use to establish cognitive links for reasoning. Such plausible relationships can be expressed via association rules. Usually, the criteria to judge the relevance of such rules are either frequency based (Bayardo & Agrawal, 1999) or causality based (for Bayesian networks, see Spirtes, Glymour, & Scheines, 1993). Here, I will pursue a different approach that aims at extracting what can be regarded as structures of knowledge — relationships that may support the inductive reasoning of agents and whose relevance is founded on information theory. The method that I will sketch in this article takes numerical relationships found in data and interprets these relationships as structural ones, using mostly algebraic techniques to elaborate structural information.

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