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.
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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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Perfilieva, I. (2021). Fuzzy-Based Methods in Data Analysis with the Focus on Dimensionality Reduction. In: Kreinovich, V. (eds) Statistical and Fuzzy Approaches to Data Processing, with Applications to Econometrics and Other Areas. Studies in Computational Intelligence, vol 892. Springer, Cham. https://doi.org/10.1007/978-3-030-45619-1_14
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DOI: https://doi.org/10.1007/978-3-030-45619-1_14
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