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Fuzzy-Based Methods in Data Analysis with the Focus on Dimensionality Reduction

  • Irina PerfilievaEmail author
Chapter
  • 6 Downloads
Part of the Studies in Computational Intelligence book series (SCI, volume 892)

Abstract

We analyze a space with a fuzzy partition and show how it determines a measure of closeness. In the space with closeness, we characterize the corresponding Laplace operator and its eigenvectors. The latter serve as projection vectors to reduce the dimension of the original space. We show that the F-transform technique can be naturally explained in the language of dimensionality reduction.

Keywords

Fuzzy partition Laplace operator F-transform Dimensionality reduction 

Notes

Acknowledgements

This work was supported by the project LQ1602 IT4Innovations excellence in science. The additional support was also provided by the project AI-Met4AI, CZ.02.1.01/0.0/0.0/17-049/0008414.

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Copyright information

© The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2021

Authors and Affiliations

  1. 1.Institute for Research and Applications of Fuzzy ModelingUniversity of OstravaOstrava 1Czech Republic

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