Out-of-Sample Extension of the Fuzzy Transform

This paper addresses the definition and computation of the out-of-sample membership functions and the resulting outof-sample FT, which extend their discrete counterparts to the continuous case. Through the out-of-sample FT, we introduce a coherent analysis of the discrete and continuous FTs, which i...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems Vol. 32; no. 3; pp. 1 - 10
Main Author: Patane, Giuseppe
Format: Journal Article
Language:English
Published: New York IEEE 01.03.2024
The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subjects:
Approximation
Color
Data analysis
Data-driven membership functions
Eigenvalues and eigenfunctions
Eigenvectors
Interpolation
Kernel
Laplace equations
Radial basis function
Radial basis functions
Signal approximation
Signal reconstruction
Three-dimensional displays
Transforms
ISSN:1063-6706, 1941-0034
Online Access:Get full text
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Summary:This paper addresses the definition and computation of the out-of-sample membership functions and the resulting outof-sample FT, which extend their discrete counterparts to the continuous case. Through the out-of-sample FT, we introduce a coherent analysis of the discrete and continuous FTs, which is applied to extrapolate the behaviour of the FT on new data and to achieve an accurate approximation of the continuous FT of signals on arbitrary data. To this end, we apply either an approximated approach, which considers the link between integral kernels and the spectrum of the corresponding Gram matrix, or an interpolation of the discrete kernel eigenfunctions with radial basis functions. In this setting, we show the generality of the proposed approach to the input data (e.g., graphs, 3D domains) and signal reconstruction
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ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2023.3326657