Advertisement

Detection of Blocks in a Binary Matrix — A Bayesian Approach

  • W. Vach
  • K. W. Alt
Conference paper
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Summary

A binary matrix representing the presence of traits and objects is given. We consider the task to detect a subblock of traits and objects such that for each trait its frequency of occurrence within these objects is highly increased. A Bayesian framework is specified and the Gibbs sampler is used to approximate the posterior distribution. The necessary extensions to use this procedure for kinship analysis in prehistoric anthropology are outlined.

Keywords

Posterior Distribution Prior Distribution Bayesian Framework Binary Matrix Kinship Analysis 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. ALT, K.W. (1991): Verwandschaftsanalyse an Skelettmaterial – Methodenentwicklung auf der Basis odontologischer Merkmale. Medizinische Habilitationsschrift Freiburg. Gustav Fischer Verlag (in press).Google Scholar
  2. ALT, K.W. & VACH, W. (1991): The Reconstruction of “Genetic Kinship” in Prehistoric Burial Complexes – Problems and Statistics. In: Bock, H.H., Ihm, P.(eds): Classification, Data Analysis, and Knowledge Organization. Springer, 299–310.Google Scholar
  3. ALT, K.W. & VACH, W. (1992): Non-Spatial Analysis of “Genetic Kinship” in Skeletal Remains. In: Schader, M. (ed): Analysing and Modeling Data and Knowledge. Springer, 247–256.Google Scholar
  4. ARABIE, P., BOORMAN, S.A. & LEVITT, P.R. (1978): Constructing block models: How and why. Journal of Mathematical Psychology, 17, 21–63. CrossRefGoogle Scholar
  5. DUFFY, D.E. & QUIROZ, A.F. (1991): A permutation-based algorithm for block clustering. Journal of Classification, 8, 65–91. CrossRefGoogle Scholar
  6. GELFAND, A.E. & SMITH, A.F.M. (1990): Sampling-based approaches to calculating marginal densities. Journal of the Amer. Statist. Assoc., 85, 398–409. CrossRefGoogle Scholar
  7. GEMAN, S. & GEMAN, D. (1984): Stochastic relaxation, Gibbs distributions and the Bayesian restoration of images. IEEE Transactions on Pattern Analysis and Machine Intelligence, 6, 721–741. CrossRefGoogle Scholar
  8. GREENACRE, M. (1984): Theory and application of correspondence analysis. Academic Press.Google Scholar
  9. HARTIGAN, J.A. (1972): Direct Clustering of a Data Matrix. Journal of the Amer. Statist. Assoc., 67, 123–129. CrossRefGoogle Scholar
  10. MARCOTORCHINO, F. (1987): Block Seriation Problems: A Unified Approach. Applied Stochastic Models and Data Analysis, 3, 73–91. CrossRefGoogle Scholar
  11. OPITZ, O. & SCHADER, M. (1984): Analyse qualitativer Daten: Einführung und Übersicht, Teil 1. OR Spektrum, 6, 67–83. Google Scholar
  12. VACH, W. & ALT, K.W. (1993): Detection of kinship structures in prehistoric burial sites. In: Andresen, J., Madsen, T., Scollar, I. (eds): Computing the Past. Aarhus University Press, 287–292Google Scholar

Copyright information

© Springer-Verlag Berlin · Heidelberg 1996

Authors and Affiliations

  • W. Vach
    • 1
  • K. W. Alt
    • 2
  1. 1.Institute of Medical Biometry and Medical InformaticsUniversity of FreiburgFreiburgGermany
  2. 2.Institute of Forensic MedicineDüsseldorf UniversityDüsseldorfGermany

Personalised recommendations