Constructing fuzzy graphs from examples

Article type: Research Article

Authors: Berthold, Michael R.^{a; *} | Huber, Klaus-Peter^{b; 1}

Affiliations: [a] Berkeley Initiative in Soft Computing, Computer Science Division, Department of EECS, 329 Soda Hall, University of California, Berkeley, CA 94720, USA | [b] University of Karlsruhe, Am Zirkel 2, 76128 Karlsruhe, Germany

Correspondence: [*] Corresponding author. Tel.: +1 510 642 9827; fax: + 1 510 643 7684; e-mail: berthold@cs.berkeley.edu; website: WWW:http://cs.berkeley.edu/~berthold.

Note: [1] E-mail: KlausPeter.Huber@Informatik.Uni-Karlsruhe.de

Abstract: Methods to build function approximators from example data have gained considerable interest in the past. Especially methodologies that build models that allow an interpretation have attracted attention. Most existing algorithms, however, are either complicated to use or infeasible for high-dimensional problems. This article presents an efficient and easy to use algorithm to construct fuzzy graphs from example data. The resulting fuzzy graphs are based on locally independent fuzzy rules that operate solely on selected, important attributes. This enables the application of these fuzzy graphs also to problems in high dimensional spaces. Using illustrative examples and a real world data set it is demonstrated how the resulting fuzzy graphs offer quick insights into the structure of the example data, that is, the underlying model. The underlying algorithm is demonstrated using several Java applets, which can be found under ‘Electronic annexes’ on www.elsevier.comilocate/ida.

Keywords: Fuzzy Graphs, Learning, Rule Extraction, Function Approximation, Interpretation

DOI: 10.3233/IDA-1999-3104

Journal: Intelligent Data Analysis, vol. 3, no. 1, pp. 37-53, 1999