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F-transform and Dimensionality Reduction: Common and Different

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New Trends in Aggregation Theory (AGOP 2019)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 981))

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Abstract

This contribution is focused on the connection between two theories: dimensionality reduction and the F-transform. We show how the graph Laplacian can be extracted from a fuzzy partition and how the Laplacian eigenmaps can be associated with the F-transform components in their functional forms. We analyse the spectrum of the graph Laplacian and its dependence on basic functions in a fuzzy partition. We support our theoretical results by numerical experiments.

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References

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Acknowledgement

The work of Irina Perfilieva has been partially supported by the project “LQ1602 IT4Innovations excellence in science” and by the Grant Agency of the Czech Republic (project No. 18-06915S).

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Authors and Affiliations

  1. Department of Mathematics, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Jiří Janeček

  2. IRAFM, University of Ostrava, 30. dubna 22, 701 03, Ostrava 1, Czech Republic

    Irina Perfilieva

Authors
  1. Jiří Janeček
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  2. Irina Perfilieva
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Corresponding author

Correspondence to Irina Perfilieva .

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Editors and Affiliations

  1. Faculty of Science, Palacký University, Olomouc, Czech Republic

    Radomír Halaš

  2. Systems Research Institute, Polish Academy of Science, Warsaw, Poland

    Marek Gagolewski

  3. Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

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Janeček, J., Perfilieva, I. (2019). F-transform and Dimensionality Reduction: Common and Different. In: Halaš, R., Gagolewski, M., Mesiar, R. (eds) New Trends in Aggregation Theory. AGOP 2019. Advances in Intelligent Systems and Computing, vol 981. Springer, Cham. https://doi.org/10.1007/978-3-030-19494-9_25

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