Graph theoretical representations of proximities by monotonic network analysis (MONA)

  • Bernhard Orth
Part of the Recent Research in Psychology book series (PSYCHOLOGY)


Proximity data can be represented either geometrically or graph theoretically. Graph theoretical methods, however, are typically restricted to representations in terms of trees. As an new method, monotonic network analysis (MONA) allows for more general representations of proximity data. For a given set of data, MONA yields a connected graph, weighted by positive integers and possessing a distance function in such a way that (1) the vertices represent the empirical objects, (2) the number of edges is minimal, (3) the weights are minimal, and (4) the ordering of the distances coincides at least approximately (according to some prescribed error criterion) with the ordering of the dissimilarities. The rationale of MONA will be stated, and the method will be illustrated by applications to real data.


Connected Graph Simple Path Similarity Judgement Normal Color Vision Proximity Data 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Bales, R.F. (1970). Personality and interpersonal behavior. New York: Hot, Rinehart and Winston.Google Scholar
  2. Carroll, J.D. & Wish, M. (1974). Models and methods for three-way multidimensional scaling. In D.H. Krantz, R.C. Atkinson, R.D. Luce, & P. Suppes (Eds.). Contemporary developments in mathematical psychology, Vol. II (pp. 57–105 ). San Francisco: Freeman.Google Scholar
  3. Corter, J.E. & Tversky, A. (1986). Extended similarity trees. Psychometrika, 51, 429–451.CrossRefGoogle Scholar
  4. Feger, H. (1985). Ordinal testing of component models for attitude objects. Paper presented at the Fourth European Meeting of the Psychometric Society and the Classification Societies, Cambridge, GB.Google Scholar
  5. Helm, C.E. (1959). A multidimensional ratio scaling analysis of color relations. Technical Report, Princeton University and Educational Testing Service.Google Scholar
  6. Kemeny, J.G. & Snell, J.L. (1962). Mathematical models in the social sciences. New York: Blaisdell.Google Scholar
  7. Krantz, D.H., Luce, R.D., Suppes, P. & Tversky, A. (1971). Foundations of measurement, Vol. I. New York: Academic Press.Google Scholar
  8. Orth, B. (1988). Representing similarities by distance graphs: Monotonic network analysis (MONA). In H.H. Bock: (Ed.) Classification and related methods of data analysis (pp. 489–494 ). Amsterdam: North-Holland.Google Scholar
  9. Schönemann, P.H., Dorcey, T. & Kienapple, K. (1985). Subadditive concatenation in dissimilarity judgement. Perception & Psychophysics, 38, 1–17.CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1989

Authors and Affiliations

  • Bernhard Orth
    • 1
  1. 1.Psychologisches Institut IUniversität HamburgHamburg 13F.R. Germany

Personalised recommendations