Data-Driven Modeling with Fuzzy Sets and Manifolds

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F61988987%3A17610%2F22%3AA2302DUN" target="_blank" >RIV/61988987:17610/22:A2302DUN - isvavai.cz</a>

Výsledek na webu

<a href="https://www.sciencedirect.com/science/article/pii/S0888613X22001001" target="_blank" >https://www.sciencedirect.com/science/article/pii/S0888613X22001001</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.ijar.2022.07.009" target="_blank" >10.1016/j.ijar.2022.07.009</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Data-Driven Modeling with Fuzzy Sets and Manifolds

Popis výsledku v původním jazyce

The manifold hypothesis states that the shape of the observed data is relatively simple and that it lies on a low-dimensional manifold embedded in a high-dimensional space. We contribute to the problem of data-driven modeling by treating it as an inverse problem where the model defines a Euclidean space with a Riemannian manifold structure. In particular, our contribution shows that a fuzzy set on a bounded support defines a Riemannian manifold that can be embedded in a multidimensional space where dimension is a model parameter. A noticeable advantage of the proposed approach is its connection with the values of the membership function and independence from the dimension of the data being modeled. Last but not least, we have found various formal representations of the Laplace-Beltrami operator and use its values as an estimate of the quality of the approximate solution to the inverse problem.

Název v anglickém jazyce

Data-Driven Modeling with Fuzzy Sets and Manifolds

Popis výsledku anglicky

The manifold hypothesis states that the shape of the observed data is relatively simple and that it lies on a low-dimensional manifold embedded in a high-dimensional space. We contribute to the problem of data-driven modeling by treating it as an inverse problem where the model defines a Euclidean space with a Riemannian manifold structure. In particular, our contribution shows that a fuzzy set on a bounded support defines a Riemannian manifold that can be embedded in a multidimensional space where dimension is a model parameter. A noticeable advantage of the proposed approach is its connection with the values of the membership function and independence from the dimension of the data being modeled. Last but not least, we have found various formal representations of the Laplace-Beltrami operator and use its values as an estimate of the quality of the approximate solution to the inverse problem.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

<a href="/cs/project/EF17_049%2F0008414" target="_blank" >EF17_049/0008414: Centrum pro výzkum a vývoj metod umělé intelligence v automobilovém průmyslu regionu</a><br>

Návaznosti

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

Rok uplatnění

2022

Kód důvěrnosti údajů

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

Název periodika

Inernational Journal of Approximate Reasoning

ISSN

0888-613X

e-ISSN

—

Svazek periodika

—

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

14

Strana od-do

178-191

Kód UT WoS článku

000852046200002

EID výsledku v databázi Scopus

2-s2.0-85135937343