Dimensionality Reduction: From Fuzzy Partitions to F-Transforms

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Dimensionality Reduction: From Fuzzy Partitions to F-Transforms

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

Dimensionality Reduction: From Fuzzy Partitions to F-Transforms

Popis výsledku anglicky

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.

Druh

C - Kapitola v odborné knize

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA18-06915S" target="_blank" >GA18-06915S: Nové přístupy k agregačním operátorům v analýze a zpracování dat</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2021

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název knihy nebo sborníku

Recent Developments and the New Direction in Soft-Computing Foundations and Applications

ISBN

978-3-030-47123-1

Počet stran výsledku

12

Strana od-do

399-411

Počet stran knihy

576

Název nakladatele

Springer, Cham

Místo vydání

Switzerland

Kód UT WoS kapitoly

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