Skip to main content

Mathematical Aspects of the Feature Pattern Analysis

  • Conference paper
Book cover Classification, Data Analysis, and Data Highways
  • 788 Accesses

Abstract

The Feature Pattern Analysis (FPA), as introduced by Feger (1988), is a method which analyzes a set of observed patterns with respect to co-occurrence. The mathematical formalism of the FPA and the several logically equivalent alternative forms of its representation as geometrical configurations, sets of contingencies and sets of prediction rules are described. Mathematical conditions for the uniqueness and existence of Type I and Type II FPA-solutions are discussed. A fast algorithm is developed to construct a two dimensional FPA-solution using Hasse-diagrams.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  • BJÖRNER, A., LAS VERGNAS, M., STURMFELS, B., WHITE, N., ZIEGLER, G.M. (1993): Oriented Matroids, Cambridge University Press, Cambridge.

    Google Scholar 

  • BOKOWSKI, J. (1994): On Recent Progress in Computational Synthetic Geometry. Preprint TH Darmstadt.

    Google Scholar 

  • BOKOWSI, J., KOLLEWE, W. (1992): On Representing Contexts in Line Arrangements, Order, 8, 393–403.

    Article  Google Scholar 

  • BOKOWSKI, J., STURMFELS, B. (1989): Computational Synthetic Geometry, Springer Verlag, Berlin - Heidelberg - New York

    Google Scholar 

  • BREHM, M., (1995): Grundlagen der Feature Pattern Analysis, Master Thesis.

    Google Scholar 

  • BREHM, M., (1996a): The Representation of Feature Pattern Analysis-solutions as Pseudoline-arrangements. In H. Feger and M Brehm, (eds.), (Under Review) New developments in Feature Pattern Analysis.

    Google Scholar 

  • BREHM, M., (1996b): Existence and Construction of FPA-solutions. In H. Feger and M Brehm, (eds.), (Under Review) New developments in Feature Pattern Analysis.

    Google Scholar 

  • FEGER, H. (1988): Spatial Representations of Feature Patterns. In H. H. Bock (eds.), Classification and Related Methods of Data Analysispp. 431–437. Amsterdam: North Holland.

    Google Scholar 

  • FEGER, H. (1994): Structure Analysis of Co-occurrence Data. Aachen: Shaker Verlag.

    Google Scholar 

  • GRéNBAUM, B. (1972): Arrangements and spreads, CBMS Regional Conference Series in Math., 10, Amer. Math. Soc, Providence, R.I.

    Google Scholar 

  • FOLKMAN; J. and LAWRENCE J., (1978): Oriented Matroids, J. Combinatorial Theory, Ser. B, 25, 199–236.

    Article  Google Scholar 

  • RINGEL, G. (1956): Teilungen der Ebene durch Geraden oder topologische Geraden, Math. Zeitschrift, 64, 79–102.

    Article  Google Scholar 

  • RINGEL, G. (1957): Über Geraden in allgemeiner Lage, Elemente der Mathematik, 12, 75–82.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1998 Springer-Verlag Berlin · Heidelberg

About this paper

Cite this paper

Brehm, M. (1998). Mathematical Aspects of the Feature Pattern Analysis. In: Balderjahn, I., Mathar, R., Schader, M. (eds) Classification, Data Analysis, and Data Highways. Studies in Classification, Data Analysis, and Knowledge Organization. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-72087-1_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-72087-1_14

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-63909-1

  • Online ISBN: 978-3-642-72087-1

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics