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master's thesis
Kriteriji kompleksnosti za k-means algoritam
Zagreb: University of Zagreb, Faculty of Science, 2014. urn:nbn:hr:217:213762
Šeperić, Stela
University of Zagreb
Faculty of Science
Department of Mathematics

Institutional repository: Repository of the Faculty of Science

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Šeperić, S. (2014). Kriteriji kompleksnosti za k-means algoritam (Master's thesis). Zagreb: University of Zagreb, Faculty of Science. Retrieved from https://urn.nsk.hr/urn:nbn:hr:217:213762

Šeperić, Stela. "Kriteriji kompleksnosti za k-means algoritam." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:213762

Šeperić, Stela. "Kriteriji kompleksnosti za k-means algoritam." Master's thesis, University of Zagreb, Faculty of Science, 2014. https://urn.nsk.hr/urn:nbn:hr:217:213762

Šeperić, S. (2014). 'Kriteriji kompleksnosti za k-means algoritam', Master's thesis, University of Zagreb, Faculty of Science, accessed 23 December 2024, https://urn.nsk.hr/urn:nbn:hr:217:213762

Šeperić S. Kriteriji kompleksnosti za k-means algoritam [Master's thesis]. Zagreb: University of Zagreb, Faculty of Science; 2014 [cited 2024 December 23] Available at: https://urn.nsk.hr/urn:nbn:hr:217:213762

S. Šeperić, "Kriteriji kompleksnosti za k-means algoritam", Master's thesis, University of Zagreb, Faculty of Science, Zagreb, 2014. Available at: https://urn.nsk.hr/urn:nbn:hr:217:213762

Metadata
TitleKriteriji kompleksnosti za k-means algoritam
AuthorStela Šeperić
MentorPavle Goldstein (mentor)
Committee memberPavle Goldstein (predsjednik povjerenstva)
Committee memberJuraj Šiftar (član povjerenstva)
Committee memberMiljenko Marušić (član povjerenstva)
Committee memberIvica Nakić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Science
(Department of Mathematics)
Zagreb
Defense date and country2014-07-11, Croatia
Scientific / art field,
discipline and subdiscipline		NATURAL SCIENCES
Mathematics
Abstract
U ovom radu obrađena je metoda za određivanje \(k\) u k-means algoritmu, što je vrlo česti problem u klasteriranju podataka. Pokazano je da funkcija cilja u k-means algoritmu konvergira. Nadalje, u potpoglavlju (1.3) pokazano je da su koordinate težišta skupa jednake aritmetičkim sredinama odgovarajućih koordinata elemenata tog skupa, te se u slučaju standardnog k-means algoritma novi centri određuju na takav način. U lemama smo dokazali da ako su podaci ekvidistantni, odnosno uniformno distribuirani, onda se optimizirana funkcija cilja ponaša odprilike kao \(C\cdot\frac{1}{k^2}\). Pretpostavka o ekvidistantnosti, odnosno uniformnoj distribuiranosti podataka, nije tako jaka kao pretpostavka o normalnoj distribuiranosti podataka u G-means algoritmu. Ovime smo pokazali da uz relativno nezahtjevne prepostavke, lijepo možemo opisati ponašanje funkcije cilja u ovisnosti o broju klastera \(k\). Na kraju, rezultati testiranja vrlo dobro potvrđuju naša teorijska saznanja o ponašanju funkcije cilja.
Abstract (english)
In this thesis, we have studied method for determining \(k\) in k-means algorithm, which is a well known problem. It is shown that the objective function coverges. Furthermore, a couple of lemmas proved that, if data follow a uniform distribution, then the objective function behaves as \(C\cdot\frac{1}{k^2}\). Assumption about data is not as strong as assumption in G-means algorithm which requires normal distribution of data. We have shown that with relatively limited assumptions, we can neatly describe behaviour of the objective function with respect to \(k\) - the number of clusters. Finally, a series of tests on simulated data sets confirmed our theoretical results about behaviour of the objective function.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:217:213762
Study programmeTitle: Mathematical Statistics
Study programme type: university
Study level: graduate
Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
Type of resourceText
File originBorn digital
Access conditionsOpen access
Terms of useLicence In copyright icon
Created on2019-02-13 10:17:45