Klasifikace realizací náhodných množin

Classification of Realisations of Random Sets

Type of document
diplomová práce
master thesis
Author
Bogdan Radović
Supervisor
Helisová Kateřina
Opponent
Staněk Jakub
Field of study
Lékařská technika
Study program
Lékařská elektronika a bioinformatika
Institutions assigning rank
katedra teorie obvodů


Rights
A university thesis is a work protected by the Copyright Act. Extracts, copies and transcripts of the thesis are allowed for personal use only and at one?s own expense. The use of thesis should be in compliance with the Copyright Act http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf and the citation ethics http://knihovny.cvut.cz/vychova/vskp.html
Vysokoškolská závěrečná práce je dílo chráněné autorským zákonem. Je možné pořizovat z něj na své náklady a pro svoji osobní potřebu výpisy, opisy a rozmnoženiny. Jeho využití musí být v souladu s autorským zákonem http://www.mkcr.cz/assets/autorske-pravo/01-3982006.pdf a citační etikou http://knihovny.cvut.cz/vychova/vskp.html
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Abstract
Random sets have gained significant importance in recent years as a valuable tool for modelling a wide range of phenomena in fields such as biology, geology, medicine, or material sciences. However, to the best of our knowledge, classification of their realisations has not yet been studied. In the presented work, a link between methods for random sets and functional data analysis is built that focusses on evaluating functional characteristics from individual components in the realisations based on their shape. Such obtained functional data is then used for nonparametric classification using both supervised and unsupervised approach based on k-nearest neighbours and k-means algorithms, respectively. The proposed procedures have been justified through a simulation study. Finally, the procedure is applied to medical data to show its applicability in practice.
 
Random sets have gained significant importance in recent years as a valuable tool for modelling a wide range of phenomena in fields such as biology, geology, medicine, or material sciences. However, to the best of our knowledge, classification of their realisations has not yet been studied. In the presented work, a link between methods for random sets and functional data analysis is built that focusses on evaluating functional characteristics from individual components in the realisations based on their shape. Such obtained functional data is then used for nonparametric classification using both supervised and unsupervised approach based on k-nearest neighbours and k-means algorithms, respectively. The proposed procedures have been justified through a simulation study. Finally, the procedure is applied to medical data to show its applicability in practice.
 
URI
http://hdl.handle.net/10467/113311
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