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undergraduate thesis
Spektralno grupiranje vremenskih nizova
Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing, 2017. urn:nbn:hr:168:028846
Ćesić, Antonija
University of Zagreb
Faculty of Electrical Engineering and Computing

Institutional repository: FER Repository

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Ćesić, A. (2017). Spektralno grupiranje vremenskih nizova (Undergraduate thesis). Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing. Retrieved from https://urn.nsk.hr/urn:nbn:hr:168:028846

Ćesić, Antonija. "Spektralno grupiranje vremenskih nizova." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2017. https://urn.nsk.hr/urn:nbn:hr:168:028846

Ćesić, Antonija. "Spektralno grupiranje vremenskih nizova." Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, 2017. https://urn.nsk.hr/urn:nbn:hr:168:028846

Ćesić, A. (2017). 'Spektralno grupiranje vremenskih nizova', Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, accessed 21 December 2024, https://urn.nsk.hr/urn:nbn:hr:168:028846

Ćesić A. Spektralno grupiranje vremenskih nizova [Undergraduate thesis]. Zagreb: University of Zagreb, Faculty of Electrical Engineering and Computing; 2017 [cited 2024 December 21] Available at: https://urn.nsk.hr/urn:nbn:hr:168:028846

A. Ćesić, "Spektralno grupiranje vremenskih nizova", Undergraduate thesis, University of Zagreb, Faculty of Electrical Engineering and Computing, Zagreb, 2017. Available at: https://urn.nsk.hr/urn:nbn:hr:168:028846

Metadata
TitleSpektralno grupiranje vremenskih nizova
Title (english)Spectral Clustering of Time Series
AuthorAntonija Ćesić
MentorZvonko Kostanjčar (mentor)
Committee memberZvonko Kostanjčar (predsjednik povjerenstva)
Committee memberMate Puljiz (član povjerenstva)
Committee memberStjepan Begušić (član povjerenstva)
GranterUniversity of Zagreb
Faculty of Electrical Engineering and Computing
Zagreb
Defense date and country2017-09-04, Croatia
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Computing
Scientific / art field,
discipline and subdiscipline		TECHNICAL SCIENCES
Electrical Engineering
Abstract
Grupiranje je jedna od najčešćih metoda analize podataka. Spektralno grupiranje je relativno nova metoda koja je posljednjih 10-20 godina dosta istraživana. Metoda spektralnog grupiranja zahtijeva da se podatci koje je potrebno grupirati prikažu u formi neusmjerenog grafa u kojem se težine bridova definiraju kao mjere sličnosti između podataka. Glavni alat za spektralno grupiranje je matrica Laplacijan grafa koja se dobiva iz matrice sličnosti i matrice težina. Matrica sličnosti se dobije pomoću funkcija korelacije i Gaussove funkcije. Iz te Laplacijanove matrice se dobivaju svojstveni vektori. Na kraju se metodom k-meansa dobiju klasteri iz matrice stupnjeva i matrice svojstvenih vektora. Dobivena funkcija je prvo testirana na simuliranim podacima kojima se unaprijed znao rezultat grupiranja te se na taj način potvrdila njena ispravnost. Nakon toga se funkcija primijenila na vremenskim podacima koji su bili prihodi 9 sektora s američkog tržišta. Ulaganje u tako grupirane sektore je rezultiralo isplativije od indeksa S&P500 po pitanju prihoda i preuzetog rizika.
Abstract (english)
Clustering is one of the most common methods of data analysis. Spectral Clustering is relatively new clustering method which has become popular in recent years. For the purpose of clustering the given objects (people, pixels, points...), we represented the data in a form of a weighted undirected graph where the nodes are the points in a feature space and the edges represent similarities between the points. The most important part of this clustering method is finding Laplacian matrix that is derived from the similarity matrix and weight matrix. The similarity matrix is obtained by the correlation function and the Gauss function. From these Laplacian matrices, native vectors are obtained. Finally, k-mean method gets clusters from the matrix of degrees and the matrix of the eigenvectors. The obtained function was first tested on simulated data to pre-know the result of the grouping and thus confirmed that the function is valid. After that, the function was applied to time series data which were 9 sectors revenue from the US market. Investments in such grouped sectors have resulted to be more profitable than the S&P500 index based on sector revenue and risk taken.
Keywords
Keywords (english)
Languagecroatian
URN:NBNurn:nbn:hr:168:028846
Study programmeTitle: Electrical Engineering and Information Technology
Study programme type: university
Study level: undergraduate
Academic / professional title: sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije (sveučilišni/a prvostupnik/ prvostupnica (baccalaureus/baccalaurea) inženjer/inženjerka elektrotehnike i informacijske tehnologije)
Type of resourceText
File originBorn digital
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Created on2019-03-19 13:38:22