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.
CITATION STYLE
Perfilieva, I. (2021). Fuzzy-based methods in data analysis with the focus on dimensionality reduction. In Studies in Computational Intelligence (Vol. 892, pp. 179–192). Springer. https://doi.org/10.1007/978-3-030-45619-1_14
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