Dimensionality Reduction: From Fuzzy Partitions to F-Transforms
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F21%3AA22027HY" target="_blank" >RIV/61988987:17610/21:A22027HY - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/978-3-030-47124-8_32" target="_blank" >https://doi.org/10.1007/978-3-030-47124-8_32</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/978-3-030-47124-8_32" target="_blank" >10.1007/978-3-030-47124-8_32</a>
Alternative languages
Result language
angličtina
Original language name
Dimensionality Reduction: From Fuzzy Partitions to F-Transforms
Original language description
The appropriate representation of high-dimensional data is the main focus of machine learning, pattern recognition andcomputer vision. With the same motivation, the F-transform uses fuzzy partitions in order to establish a compressed representation of data. Two distinguished properties of the F-transform: the best approximation in a local sense and dimensionality reduction contributed to the fact that the F-transform has many successful applications. We show that the technique of F-transform fully agrees with the technique of dimensionality reduction, based on Laplacian eigenmaps. To justify this claim, we characterize the processed by the F-transform data in terms of the adjacency graph that reflects their (data) intrinsic geometry. An application to the problem of image restoration is given.
Czech name
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Czech description
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Classification
Type
C - Chapter in a specialist book
CEP classification
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OECD FORD branch
10102 - Applied mathematics
Result continuities
Project
<a href="/en/project/GA18-06915S" target="_blank" >GA18-06915S: New approaches to aggregation operators in analysis and processing of data</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Book/collection name
Recent Developments and the New Direction in Soft-Computing Foundations and Applications
ISBN
978-3-030-47123-1
Number of pages of the result
12
Pages from-to
399-411
Number of pages of the book
576
Publisher name
Springer, Cham
Place of publication
Switzerland
UT code for WoS chapter
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