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Complexity reduction and approximation of multidomain systems of partially ordered data

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  • Arcagni, Alberto
  • Avellone, Alessandro
  • Fattore, Marco

Abstract

Two greedy algorithms for the synthesis and approximation of multidomain systems of partially ordered data are proposed. Given k input partially ordered sets (posets) on the same elements, the algorithms search for the optimally approximating partial orders, minimizing the dissimilarity between the generated and input posets, based on their matrices of mutual ranking probabilities. A general approximation algorithm is developed, together with a specific procedure for approximation over bucket orders, which are the natural choice when the goal is to “condense” the inputs into rankings, possibly with ties. Different loss functions are also employed, and their outputs are compared. A real example pertaining to regional well-being in Italy motivates the algorithms and shows them in action.

Suggested Citation

  • Arcagni, Alberto & Avellone, Alessandro & Fattore, Marco, 2022. "Complexity reduction and approximation of multidomain systems of partially ordered data," Computational Statistics & Data Analysis, Elsevier, vol. 173(C).
    • Handle: RePEc:eee:csdana:v:173:y:2022:i:c:s0167947322001001
    DOI: 10.1016/j.csda.2022.107520
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    References listed on IDEAS

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    8. Marco Fattore, 2016. "Partially Ordered Sets and the Measurement of Multidimensional Ordinal Deprivation," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 128(2), pages 835-858, September.
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    11. Alberto Arcagni & Elisa Barbiano di Belgiojoso & Marco Fattore & Stefania M. L. Rimoldi, 2019. "Multidimensional Analysis of Deprivation and Fragility Patterns of Migrants in Lombardy, Using Partially Ordered Sets and Self-Organizing Maps," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 141(2), pages 551-579, January.
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    1. Fattore, Marco & Alaimo, Leonardo Salvatore, 2023. "A partial order toolbox for building synthetic indicators of sustainability with ordinal data," Socio-Economic Planning Sciences, Elsevier, vol. 88(C).

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