Abstract
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.
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Acknowledgment
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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Myachin, A., Mirkin, B. (2019). Ordinal Equivalence Classes for Parallel Coordinates. In: Yin, H., Camacho, D., Tino, P., Tallón-Ballesteros, A., Menezes, R., Allmendinger, R. (eds) Intelligent Data Engineering and Automated Learning – IDEAL 2019. IDEAL 2019. Lecture Notes in Computer Science(), vol 11871. Springer, Cham. https://doi.org/10.1007/978-3-030-33607-3_56
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DOI: https://doi.org/10.1007/978-3-030-33607-3_56
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