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master's thesis
Hilbertovi prostori reproducirajućih jezgri
2021. urn:nbn:hr:166:798236
Buljan, Antonio
University of Split
University of Split, Faculty of science
Department of Mathematics

Cite this document

Buljan, A. (2021). Hilbertovi prostori reproducirajućih jezgri (Master's thesis). Retrieved from https://urn.nsk.hr/urn:nbn:hr:166:798236

Buljan, Antonio. "Hilbertovi prostori reproducirajućih jezgri." Master's thesis, University of Split, University of Split, Faculty of science, 2021. https://urn.nsk.hr/urn:nbn:hr:166:798236

Buljan, Antonio. "Hilbertovi prostori reproducirajućih jezgri." Master's thesis, University of Split, University of Split, Faculty of science, 2021. https://urn.nsk.hr/urn:nbn:hr:166:798236

Buljan, A. (2021). 'Hilbertovi prostori reproducirajućih jezgri', Master's thesis, University of Split, University of Split, Faculty of science, accessed 21 May 2022, https://urn.nsk.hr/urn:nbn:hr:166:798236

Buljan A. Hilbertovi prostori reproducirajućih jezgri [Master's thesis]. Split: University of Split, University of Split, Faculty of science; 2021 [cited 2022 May 21] Available at: https://urn.nsk.hr/urn:nbn:hr:166:798236

A. Buljan, "Hilbertovi prostori reproducirajućih jezgri", Master's thesis, University of Split, University of Split, Faculty of science, Split, 2021. Available at: https://urn.nsk.hr/urn:nbn:hr:166:798236

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Metadata
TitleHilbertovi prostori reproducirajućih jezgri
Title (english)Reproducing kernel Hilbert spaces
AuthorAntonio Buljan
MentorVesna Gotovac Đogaš (mentor)
Committee memberVesna Gotovac Đogaš (predsjednik povjerenstva)
Committee memberGoran Erceg (član povjerenstva)
Committee memberAna Laštre (član povjerenstva)
GranterUniversity of Split
University of Split, Faculty of science
(Department of Mathematics)
Split
Defense date and country2021-09-30, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu upoznajemo se s teorijom Hilbertovih prostora reproducirajućih jezgri te objašnjavamo matematičku pozadinu primjene jezgrenih funkcija u umjetnoj inteligenciji. Istražujemo vezu između pozitivno semidefinitnih funkcija i jezgrenih funkcija te svojstva različitih pozitivno semidefinitnih funkcija na proizvoljnom skupu. U prvom poglavlju uvodimo pojam potpunih metričkih, normiranih te unitarnih prostora i istražujemo njihova svojstva. U drugom poglavlju gradimo teoriju Hilbertovih prostora reproducirajućih jezgri, a u zadnjem poglavlju pokazujemo kako se navedena teorija primjenjuje u umjetnoj inteligenciji.
Abstract (english)
In this thesis, we introduce the theory of reproducing kernel Hilbert spaces and explain the mathematical background of the application of kernel functions in artificial intelligence. We investigate the relationship between positive semidefinite functions and kernel functions and the properties of different positive semidefinite functions on an arbitrary set. In the first chapter, we introduce the concept of complete metric, normed and pre-Hilbert spaces and explore their properties. In the second chapter we build a theory of reproducing kernel Hilbert spaces and in the last chapter we show how this theory is applied in artificial intelligence.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:166:798236
Study programmeTitle: Mathematics; specializations in: major in pure mathematics, major in computing, major in teaching, major in statistics and computing
Course: major in computing
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsAccess restricted to students and staff of home institution
Terms of useLicence In copyright icon
Created on2021-10-22 11:10:48