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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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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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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DOI: https://doi.org/10.1007/978-3-030-19494-9_25
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-030-19494-9
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