Data-Driven Fuzzy Transform

The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., 2-D images), thus, limiting its potential application to arbitrary data in terms of dimensionality and structure. This article defines and analyzes the properties of the data-driven F-transform, with...

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Vydáno v:IEEE transactions on fuzzy systems Ročník 30; číslo 9; s. 3774 - 3784
Hlavní autor: Patane, Giuseppe
Médium: Journal Article
Jazyk:angličtina
Vydáno: New York IEEE 01.09.2022
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Témata:
Adaptation models
Chebyshev approximation
Chebyshev polynomials
data-driven Fuzzy-transform (F-transform)
data-driven membership functions
F-transform
Kernel
Laplace equations
Laplacian spectrum
Linear systems
Operators (mathematics)
Polynomials
Splines (mathematics)
Transforms
ISSN:1063-6706, 1941-0034
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Shrnutí:The Fuzzy transform is applied mainly to 1-D signals and 2-D data organized as a regular grid (e.g., 2-D images), thus, limiting its potential application to arbitrary data in terms of dimensionality and structure. This article defines and analyzes the properties of the data-driven F-transform, with a focus on the construction of the class of data-driven membership functions, which are multiscale, local, linearly independent, intrinsic, and robust to data discretization. Data-driven membership functions are defined by applying a 1-D filter to the Laplace-Beltrami operator, which encodes the geometric and topological properties of the input data. Then, we address the efficient computation of the data-driven F-transform through a polynomial or a rational polynomial approximation of the input filter. In this way, the computation of the data-driven F-transform is independent of the evaluation of the membership functions at any point of the input domain and reduces to the solution of a small set of sparse and symmetric linear systems. Finally, the data-driven F-transform is efficiently evaluated on large and arbitrary data, in terms of dimensionality, structure, and size.
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2021.3128684