Ordinal Equivalence Classes for Parallel Coordinates

  • Alexey Myachin
  • Boris MirkinEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11871)


We give a mathematical treatment to the concept of ordinal equivalence defined relative to all m! possible permutations of parallel axes. We prove that the ordinal equivalence is determined by the pair-wise co-monotonicity equivalence relations, thus leading to simple algorithmic procedures for finding the corresponding partition. Each ordinal equivalence class can be visualized as a profile of co-monotone polylines, in this way preventing any clutter at the image. We illustrate our approach with two datasets taken from the literature.


Parallel coordinates Co-monotonicity Ordinal equivalence Clutter 



The authors acknowledge continuing support by the Academic Fund Program at the National Research University Higher School of Economics (grant №19-04-019 in 2018-2019) and by the International Decision Choice and Analysis Laboratory (DECAN) NRU HSE, in the framework of a subsidy granted to the HSE by the Government of the Russian Federation for the implementation of the Russian Academic Excellence Project “5-100”.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.National Research University Higher School of EconomicsMoscowRussia
  2. 2.Institute of Control Science of Russian Academy of ScienceMoscowRussia

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