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Classification and Seriation by Iterative Reordering of a Data Matrix

  • Richard Streng
Part of the Studies in Classification, Data Analysis, and Knowledge Organization book series (STUDIES CLASS)

Abstract

A heuristic algorithm is presented which searches for the reordering of rows and columns of a symmetric similarity matrix in order to fulfill, at least approximatively, the Robinson condition. The algorithm uses pairwise interchanges in constructive and iterative strategies. — A rectangular m×n matrix of two different sets of parameters can be treated by first converting or preprocessing the data into two square similarity matrices, each for rows and columns, before applying the above mentioned technique. The resulting orderings for rows and columns in the m×n matrix yields a pattern whose underlying structure can be interpreted by inspection. — Agglomerative hierarchical classification can be obtained after the rearrangement using only neighbouring objects (rows, columns). — A computer program has been implemented with a fast reordering algorithm and a graphical dendrogram presentation.1

Keywords

Similarity Matrix Main Diagonal Knowledge Organization Neighbouring Classis Rectangular Matrix 
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.

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References

  1. Arabie, P., Boorman, S. A., Levitt, R. (1978): Constructing blockmodels: how and why. J. Math. Psychol. 17 21–63.zbMATHCrossRefGoogle Scholar
  2. Arabie, P., Hubert, L. J. (1990): The bond energy algorithm revisited. IEEE Transactions on Systems, Man, and Cybernetics 20 268–274.Google Scholar
  3. Bertin, J. (1980): Traitements graphiques et mathémathiques. Différence fondamentale et complémentaire. Mathématiques et Sciences Humaines 7 60–71.Google Scholar
  4. Caraux, G. (1984): Réorganisation et représentation visuelle d’une matrice de données numériques: un algorithme itératif. Revue de Statistique Appliquée 32 5–23.Google Scholar
  5. Deichsel, G., Trampisch H. J. (1985): Clusteranalyse und Diskriminanzanalyse. G. Fischer, Stuttgart.Google Scholar
  6. Diday, E. (1987): Orders and overlapping clusters by pyramids. Inria, B.P. 105, 78153 Le Chesnay Cedex (France) 0–33.Google Scholar
  7. Fitch, W. M., Margoliash, E. (1967): Construction of phylogenetic trees. Science 155 279–284.CrossRefGoogle Scholar
  8. Hubert, L., Schultz, J. (1976): Quadratic assignment as a general data analysis strategy. Br. J. math. statist. Psychol. 29 190–241.zbMATHMathSciNetGoogle Scholar
  9. Jaccard, P. (1908): Nouvelles recherches sur la distribution florale. Bull. Soc. Vaud. Sci. Nat., t. 44 223–270.Google Scholar
  10. Leuschner, D. (1974): Einführung in die numerische Taxonomie. G. Fischer, Jena.Google Scholar
  11. Marcotorchino, F. (1987): Block seriation problems: a unified approach. Applied Stochastic Models and Data Analysis 3 73–91.zbMATHCrossRefGoogle Scholar
  12. Mccormick, JR. W. T., Schweitzer, P. J., WHITE,T. W. (1972): Problem decomposition and data reorganization by a clustering technique. Oper. Res. 20 993-1009.Google Scholar
  13. Meissner, J. D. (1978): Heuristische Programmierung. Akad. Verlagsgesellschaft Wiesbaden. MüLLER-Merbach, H. (1970): Optimale Reihenfolgen. Berlin, Heidelberg, New York.Google Scholar
  14. Robinson, W. S. (1951): A method for chronologically ordering archaeological deposits. American Antiquity 16 293–301.CrossRefGoogle Scholar
  15. Sokal, R. R., Sneath, P. H. (1963): Principles of numerical taxonomy, San Francisco: Freeman.Google Scholar
  16. Sørensen, T. (1948): A method of establishing groups of equal amplitude in plant sociology based on similarity of species content. Det Kongelige Danske Videnskabernes Selskab Biol. Skr. 5(4) 1–34.Google Scholar
  17. Spaulding, A. C. (1970): Some elements of quantitative archaeology. In: F. R. Hodson, D. G. Kendall, and P. Tautu, (Eds.) Mathematics in the Archaeological and Historical Sciences. Edinburgh University Press. 3–16.Google Scholar
  18. Streng R., Schönfelder P. (1978): Ein heuristisches Computer-Programm zur Ordnung pflanzensoziologischer Tabellen. Hoppea, Denkschr. Regensb. Bot. Ges., 5 407–433.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Richard Streng
    • 1
  1. 1.Institute for ZoologyUniversity of RegensburgRegensburgGermany

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