×

Saturated systems of homogeneous boxes and the logical analysis of numerical data. (English) Zbl 1078.62503

Summary: Following the general principles of the logical analysis of data methodology, originally developed for the case of binary data, we define a similar approach for the analysis of numerical data. The central concepts of this methodology are those of homogeneous boxes and of saturated systems of homogeneous boxes. The box-clustering heuristic described in this paper is efficient and was applied successfully for the analysis of datasets concerning breast tumors, oil exploration and diabetes.

MSC:

62-07 Data analysis (statistics) (MSC2010)
68P99 Theory of data
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Boros, E.; Hammer, P.L.; Ibaraki, T.; Kogan, A.; Mayoraz, E.; Muchnik, I., An implementation of logical analysis of data, IEEE trans. knowledge data eng., 12, 2, 292-306, (2000)
[2] Crama, Y.; Hammer, P.L.; Ibaraki, T., Cause-effect relationships and partially defined Boolean functions, Ann. oper. res., 16, 299-325, (1988) · Zbl 0709.03533
[3] P.L. Hammer, Partially defined Boolean functions and cause-effect relationships, Lecture at the International Conference on Multi-Attribute Decision Making Via Or-Based Expert Systems, University of Passau, Germany, April 1986.
[4] P.L. Hammer, A. Kogan, B. Simeone, S. Szedmák, Pareto-optimal patterns in logical analysis of data, RUTCOR Research Report, 7-2001.
[5] Mitchell, T., Machine learning, (1997), McGraw-Hill New York · Zbl 0913.68167
[6] Murthy, S.K.; Kasif, S.; Salzberg, S., A system for induction of oblique decision trees, J. artif. intel. res., 2, 1-32, (1994) · Zbl 0900.68335
[7] J.W. Smith, J.E. Evelhart, W.C. Dickinson, W.C. Knowler, R.S. Johannes, Using the Adap learning algorithm to forecast the onset of diabetes mellitus, in: Proceedings of the Symposium on Computer Applications and Medical Care, IEEE Computer Society Press, Silver Spring, MD, 1988, pp. 261-265.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.