Klasteriranje k-sredinama

master's thesis

• Author: Petar Apolonio
• Mentor: Zlatko Drmač (mentor)
• Committee member: Zlatko Drmač (predsjednik povjerenstva)
• Committee member: Vjeran Hari (član povjerenstva)
• Committee member: Hrvoje Šikić (član povjerenstva)
• Committee member: Zvonimir Bujanović (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2018-03-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom radu prikazan je algoritam klasteriranja \(k\) - sredinama. Započinje davanjem osnovnih pojmova i opisom podjele algoritama klasteriranja na hijerarhije i particijske. U nastavku se opisuju osnovni algoritam \(k\) - sredina i njegove varijacije: fuzzy \(k\) - sredine, sferne \(k\) - sredine, jezgrene \(k\) - sredine i harmonijske \(k\) - sredine. Također, za sferne \(k\) - sredine je prikazano unaprjeđenje metodom prve varijacije, dok za jezgrene \(k\) - sredine je prikazana nadogradnja uvođenjem težina. Na kraju rada je prikazana kvantizacija boja na slikama pomoću osnovnog algoritma \(k\) - sredina, te usporedba jezgrenog i osnovnog algoritma na primjeru. U dodatku se nalaze kodovi napisani u programskom okruženju MATLAB pomoću kojih su se dobili primjeri u trećem poglavlju.

Abstract (english)

This paper presents \(k\) - means clustering algorithm. It starts with basic concepts and it gives description of division of clustering algorithms into hierarchical and partitioning. Further, basic \(k\)-means algorithm and few of its variations such as Fuzzy \(k\)-means, Spherical \(k\)-means, Kernel \(k\)-means and Harmonic \(k\)-means, are described. Also, for Spherical \(k\)-means it’s described improvement with First Variation method, and for Kernel \(k\)-means it is described upgrade by bringing weights into algorithm. At the end of this paper it is shown how we can do quantization of color in the images with basic \(k\)-means algorithm environment. Also, comparison between basic and Kernel \(k\)-means algorithms is given using an example. The Appendix contains MATLAB codes which are used to make examples in 3rd chapter.

• Keywords: algoritma klasteriranja; k-sredine; \(k\)-sredine; kvantizacija boja; MATLAB
• Keywords (english): clustering algorithm; k-means; \(k\)-means; quantization of color; MATLAB
• Language: croatian
• URN:NBN: urn:nbn:hr:217:446221
• Study programme: Title: Mathematical Statistics; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra matematike (magistar/magistra matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2018-07-10 09:56:10