Hasse Diagrams Based on Transformed Data Matrices

  • Rainer Brüggemann
  • Ganapati P. Patil
Part of the Environmental and Ecological Statistics book series (ENES)


We have seen in Chapter 5 as to why and how the structure of partial order (X, IB) can be related to properties of the data matrix. However, partial order with many objects can lead to messy Hasse diagrams with too many lines hiding the structure. What may be the reason for complexity in such diagrams? The number of objects |X| is not necessarily causing messy Hasse diagrams because chains of height |X| or antichains of width |X| certainly allow clear visualizations. There is another reason for complexity: In partial orders, we obtain either x < y or x || y even if the numerical difference ɛ between attribute values is small:


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of EcohydrologyLeibniz Institute of Freshwater Ecology and Inland FisheriesSchöneicheGermany
  2. 2.Center for Statistical Ecology and Environmental StatisticsPennsylvania State UniversityUniversity ParkUSA

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